https://wiki.randaldouc.xyz/ 2026-05-15T21:19:41+0200 https://wiki.randaldouc.xyz/ https://wiki.randaldouc.xyz/lib/tpl/dokuwiki/images/favicon.ico text/html 2023-06-14T15:41:42+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:15062023&rev=1686750102&do=diff Séminaire SOP et Journée des doctorants 2A TSP (15/06/2023) Lieu: F018, Telecom Sudparis. Horaire Orateur Titre Abstract $(x, y)$$x$$y$ text/html 2026-02-05T08:02:32+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:approximation-lemma&rev=1770274952&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2023-04-14T14:04:39+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:beta_distribution&rev=1681473879&do=diff distribution $\newcommand{\rset}{\mathbb R} \newcommand{\1}{\mathsf{1}} \newcommand{\rme}{\mathrm{e}} \newcommand{\rmd}{\mathrm{d}} \newcommand{\mcb}{\mathcal{B}} \newcommand{\PE}{\mathbb{E}} \newcommand{\eqsp}{\;} $ The Gamma distribution has the following density $$ x\mapsto \frac{b^a}{\Gamma(a)}\,x^{a-1}\,\rme^{- b x}\,\1_{\rset_+}(x)\;, \quad\text{with}\quad\Gamma(a)=\int_0^\infty x^{a-1}\,\rme^{-x}\,\rmd x \;. $$ It is easy to check that $\Gamma(k)=(k-1)!$ and, by integration by parts… text/html 2025-10-03T09:06:11+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:boule&rev=1759475171&do=diff Question Let $D$ be an infinite set without accumulation points in $\mathbb{R}^d$. Show that, for every $n \in \mathbb{N}^*$, there exists a ball containing exactly $n$ points of $D$. Proof First, note that $D$ must be countable. Indeed, for each point $x \in D$, one can associate a rational ball (that is, a ball with rational center coordinates and rational radius) containing $x$$D$$D$$D$$(a,b) \in D \times D$$$ H_{a,b} = \{ x \in \mathbb{R}^d \; ; \; \|x-a\| = \|x-b\| \}. $$$$ G = \bigc… text/html 2022-03-16T07:40:22+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:characteristic_function_gaussian&rev=1647412822&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2024-06-20T15:02:26+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:coupling&rev=1718888546&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2025-09-30T13:18:18+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:datascience&rev=1759231098&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2026-02-07T12:44:14+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:de-finetti&rev=1770464654&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2022-09-01T08:44:22+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:education&rev=1662014662&do=diff POSITION * Janvier 2008- Professeur à Telecom SudParis. Depuis 2017, professeur chargé de cours temps partiel à l'Ecole Polytechnique. * Septembre 2001-2007 Professeur chargé de cours temps complet à l’Ecole Polytechnique. RECHERCHE * text/html 2024-09-04T11:05:49+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:emacs-essentiel&rev=1725440749&do=diff Commandes essentielles pour Emacs Emacs est un éditeur de texte très puissant et extensible. Il offre une large gamme de commandes pour naviguer, éditer et manipuler du texte. Voici les commandes essentielles pour travailler efficacement avec Emacs. text/html 2025-07-09T17:33:27+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:emines&rev=1752075207&do=diff Cours de Régression et Classification supervisée Syllabus Objectif : Ce cours combine une approche pratique (modélisation, entraînement, validation de modèles) et une approche théorique rigoureuse, permettant aux étudiants de : * Comprendre les principes mathématiques sous-jacents aux algorithmes text/html 2025-10-10T17:55:24+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:emines2025&rev=1760111724&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2022-04-28T14:27:14+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:enigmahanoi&rev=1651148834&do=diff funny exercise enigma A first illustrative example $1/2$ $ \newcommand{\rset}{\mathbb R} \newcommand{\PP}{\mathbb P}$$X$$\alpha: \rset \to (0,1)$$\alpha(X)$ $X_0$$X_1$$X=X_0$$1-\alpha(X_0)$$X=X_1$$\alpha(X_1)$$\PP(X=X_0)=\PP(X=X_1)=1/2$$$ \PP(\mbox{right answer})= \frac12 (1-\alpha(X_0))+\frac12 \alpha(X_1)=\frac12+ \underbrace{\frac{\alpha(X_1)-\alpha(X_0)}{2}}_{>0} >\frac12 $$ $X$$\mu$$\mathcal B(\rset)$$\mu([a,b])>0$$a,b \in \rset$$a\neq b$$Y$$\mu$$X<Y$$X>Y$...$$ \PP(\mbox{right answer})=\… text/html 2024-10-08T00:22:21+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:exo&rev=1728339741&do=diff text/html 2022-03-16T07:40:22+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:exobrownian&rev=1647412822&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2022-03-16T07:40:22+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:exofourier&rev=1647412822&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2025-09-04T00:59:01+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:extra&rev=1756940341&do=diff Formation théâtrale et cinématographique * Stage avec Azize Kabouche, Théâtre de l’Est Parisien, sur des textes de Catherine Anne, Lars Noren, Joël Pommerat, 2010-2011. * Stage et coaching par Pascal Luneau au Studio Pygmalion pour la préparation du film « Barrage contre le pacifique », 2007. text/html 2026-02-07T15:03:33+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:forward-downward-martingale&rev=1770473013&do=diff Upcrossing Inequality and Martingale Convergence Doob's Upcrossing Inequality Let $a<b$ and let $(X_k)_{k\ge0}$ be a real-valued process. We define an indicator process $(C_k)$ that tracks the phases during which the process is performing an upcrossing from $a$ to $b$. Set $$ C_0 := \mathbf 1_{\{X_0<a\}}. $$ For all $k\ge1$$$ C_k = \mathbf 1_{\{C_{k-1}=1\}}\mathbf 1_{\{X_{k-1}\le b\}} + \mathbf 1_{\{C_{k-1}=0\}}\mathbf 1_{\{X_{k-1}<a\}}. $$$$ Y_k := \sum_{\ell=1}^k C_\ell (X_\ell - X_{\ell-… text/html 2023-02-08T17:53:45+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:gan_readme&rev=1675875225&do=diff Projet Cassiopée: Etude théorique et pratique des Réseaux Antagonistes Génératifs (GANs) Contenu Théorique * Lecture et restitution du papier principal Some theoretical properties of GANs par G. Biau, B. Cadre, M. Sangnier et U. Tanielan. * Lectures complémentaires: * text/html 2022-03-16T07:40:22+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:gauss_markov&rev=1647412822&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2022-11-17T17:53:00+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:gausslipshitz&rev=1668703980&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2026-02-06T13:06:46+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:hewitt-savage&rev=1770379606&do=diff Hewitt-Savage 0-1 Law Let \((X_i)_{i\in\mathbb{N}}\) be a family of independent and identically distributed (i.i.d.) random variables defined on a common probability space and taking values in a measurable space \((\mathsf{X}, \mathcal{X})\). Equivalent Formulation: We can also consider \(X_i\) as the coordinate projection associated with the probability space \((\mathsf{X}^\mathbb{N}, \mathcal{X}^{\otimes\mathbb{N}}, \mathbb{P})\)\(\mathbb{P}\)\((X_i)\)\(n \in \mathbb{N}\)\(\mathcal{G}_n\)\(f… text/html 2026-04-17T11:27:21+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:homepage&rev=1776418041&do=diff Welcome to Randal Douc's homepage * Current position: Full professor at Telecom Sudparis (2008-current). * Former position: * Full time position: “Professeur chargé de cours”, Ecole Polytechnique, 2001-2007. * Part-time position: “Professeur chargé de cours”, Ecole Polytechnique, 2017-2023. text/html 2022-03-16T07:40:22+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:inverse_fourier&rev=1647412822&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2022-03-16T07:40:22+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:itc&rev=1647412822&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2026-04-09T23:17:03+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:kkt&rev=1775769423&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2023-11-05T18:04:32+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:knn&rev=1699203872&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2023-11-15T00:23:54+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:kolmogorov&rev=1700004234&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2026-04-11T08:26:45+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:krein&rev=1775888805&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2023-11-10T10:19:07+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:kullback&rev=1699607947&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2023-02-07T10:48:05+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:lda&rev=1675763285&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2024-09-04T10:40:47+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:linux-essentiel&rev=1725439247&do=diff Commandes essentielles en Terminal Linux Voici les commandes essentielles pour le Terminal sur Linux. Elles couvrent les bases de la gestion des fichiers, des processus, de la navigation et de l'administration du système. Commandes de navigation text/html 2026-02-23T19:10:53+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:lln&rev=1771870253&do=diff law_of_large_numbers A short proof of the Strong Law of Large Numbers... Statement $$ \newcommand{\PE}{\mathbb E} \newcommand{\PP}{\mathbb P} \newcommand{\eqsp}{\quad} \newcommand{\nset}{\mathbb N} $$ Theorem: Strong Law of Large numbers. If $(X_i)$ are iid random variables and $\PE[|X_1|]<\infty$, then $$ \lim_{n \to \infty} n^{-1} \sum_{i=1}^n X_i=\PE[X_1]\eqsp a.s. $$ We follow the approach of Bernard Delyon in his unpublished lecture notes on dynamical systems. We just made minor adapt… text/html 2025-07-09T11:02:24+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:log-sobolev&rev=1752051744&do=diff Logarithmic Sobolev inequality and concentration $\newcommand{\Ent}{\mathrm{Ent}}$ Theorem * Taken from Thm 7.4.1 in the book “Sur les inégalités de Sobolev logarithmiques”. Let $\mu$ be a probability measure on $\mathbb{R}^n$ satisfying the following logarithmic Sobolev inequality: $$ \forall f \in C_b^\infty(\mathbb{R}^n), \quad \Ent_\mu(f^2) \leq c \, \mathbb{E}_\mu(|\nabla f|^2), $$ then for every Lipschitz function $F : \mathbb{R}^n \to \mathbb{R}$$\|F\|_{\mathrm{Lip}} \leq 1$$r > 0$$… text/html 2022-03-16T07:40:23+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:logdet&rev=1647412823&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2022-08-24T12:18:01+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:map594&rev=1661336281&do=diff Soutenance de stage MAP 594 La soutenance consistera en 20 mns de présentation et 10 minutes de questions. Date horaire Nom complet de l'étudiant Lien Visio pour la soutenance 24/08 16H45 Roland Nzala-Backa text/html 2022-03-16T07:40:23+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:marcinkiewicz&rev=1647412823&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2025-12-16T16:31:03+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:markovchains&rev=1765899063&do=diff markov_chains A course on Markov Chains: Advanced topics * Trick: The real address of this page is: <https://wiki.randaldouc.xyz/doku.php?id=world:markovchains> but there is also an equivalent (more simple) address: <https://lstu.fr/markovchains> Registration to the course * Please register here Program of the course * Where? Institut de Mathématiques d'ORSAY. Room: 1A14. text/html 2022-03-16T07:40:23+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:martingale&rev=1647412823&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2025-09-30T13:19:23+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:mat3101&rev=1759231163&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2022-03-16T07:40:23+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:max&rev=1647412823&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2025-10-17T12:53:07+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:mcmc&rev=1760698387&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2023-10-07T12:32:24+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:measure&rev=1696674744&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2025-01-29T09:44:36+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:minkovski&rev=1738140276&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2026-03-28T12:58:30+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:mva&rev=1774699110&do=diff Stochastic calculus for Machine Learning Registration to the course * Please register here Program of the course * Where? ENS Paris-Saclay. * When? Topics Material text/html 2024-03-27T17:27:31+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:non-geometric&rev=1711556851&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2023-11-04T14:03:44+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:optimal-classifier&rev=1699103024&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2022-04-19T23:04:48+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:pageperso&rev=1650402288&do=diff Welcome to Randal Douc's homepage * Current position: Full professor at Telecom Sudparis (2008-current). * Former position: * Full time position: “Professeur chargé de cours”, Ecole Polytechnique, 2001-2007. * Part-time position: “Professeur chargé de cours”, Ecole Polytechnique, 2017-2023. text/html 2026-05-06T01:15:42+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:pagereponse&rev=1778022942&do=diff text/html 2026-05-06T01:15:08+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:pagereponsemultiple&rev=1778022908&do=diff text/html 2023-10-18T16:52:08+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:partition&rev=1697640728&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2022-11-13T18:38:42+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:pca&rev=1668361122&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2025-07-08T16:52:31+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:pinsker&rev=1751986351&do=diff The Pinsker Inequality. $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condt… text/html 2024-01-20T09:47:39+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:projet-mda-2024&rev=1705740459&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2026-01-27T19:53:32+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:projet-mda-2025&rev=1769540012&do=diff Projects * Click here to switch back to the Markov chain course website The defense schedule * Room: 1A13 (equipped with videoprojector). Time (p.m.) Team 2:00-2:30 Audibert-Gabet 2:30-3:00 Bastin-Belkacemi 3:00-3:30 Bichard-Cros 3:30-4:00 Poblete text/html 2025-09-13T13:53:48+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:publi-citi&rev=1757764428&do=diff ~~HTML~~ <script> fetch(“<https://api.archives-ouvertes.fr/search/?q=structId_i:89901&wt=json&sort=producedDate_tdate+desc>”) .then(response => response.json()) .then(data => { let html = ""; data.response.docs.forEach(doc => { let title = doc.title_s || "Titre non disponible"; let authors = (doc.authFullName_s || []).join(", "); let date = doc.producedDate_s || ""; let link = doc.uri_s || "#"; html += `<div class="publication"> <h3><a href="$… text/html 2022-04-22T09:13:41+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:question&rev=1650611621&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2025-09-30T19:02:18+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:quiz1&rev=1759251738&do=diff Day 1 We observe \((x_i,y_i)\) for \(i \in [1:n]\) where \(y_i=\beta_1 + \beta_2 x_i+\epsilon_i\) for \(i \in [1:n]\). We assume that there exists \(i\neq j\), such that \(x_i\neq x_j\) and \(\mathbb{E}[\epsilon_i]=0\) and \(\mathbb{C}\mathrm{ov}(\epsilon_i,\epsilon_j)=\sigma^2 \mathbf{1}(i \neq j)\). We use the notation: \(\bar x=\sum_{i=1}^n x_i/n\) and \(\bar y=\sum_{i=1}^n y_i/n\). Which of the following statements are always true: Number statement … text/html 2025-10-01T22:14:23+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:quiz2&rev=1759349663&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2025-10-03T00:54:42+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:quiz3&rev=1759445682&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2025-10-06T09:30:58+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:quiz4&rev=1759735858&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2025-10-06T23:27:17+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:quiz5&rev=1759786037&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2026-01-19T15:42:47+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:raccourcis&rev=1768833767&do=diff List of useful shortcuts and tricks Clavier Mx keys mini * Si le clavier clignote, taper Fn echap. Essentiel * Commandes essentielles en Terminal Linux * Commandes essentielles pour l'éditeur vi Brave * Ctrl shift O: liste des favoris... Tig * tig puis s pour voir le statut puis ! devant le fichier changé pour retrouver l'ancienne version $\theta \in \Theta$ text/html 2022-03-16T07:40:23+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:radon&rev=1647412823&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2023-04-18T14:58:10+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:random-walk&rev=1681822690&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2023-04-20T08:57:41+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:ratio-of-uniform&rev=1681973861&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2024-02-06T21:54:17+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:rdv-rapport&rev=1707252857&do=diff Proposition de rdv pour Wojciech, François et Yohan: Randal: je vous propose 1 heure en zoom pour remplir ensemble certaines rubriques du rapport. Voici mes prochaines disponibilités. Si vous pouviez ecrire vos initiales dans la rubrique Qui?, ca serait super text/html 2022-04-11T13:42:40+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:reflectional_coupling&rev=1649677360&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2023-02-10T18:17:16+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:robbins_monro&rev=1676049436&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2022-03-16T07:40:23+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:sigmafield&rev=1647412823&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2023-09-11T14:54:33+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:soutenance-map594&rev=1694436873&do=diff Soutenance de stage MAP594 Date Horaire Nom du stagiaire Prénom du stagiaire lien visio Si la soutenance dure plus que 40 mns, veuillez vous reconnecter ici text/html 2025-11-21T17:07:01+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:std2025_abstract&rev=1763741221&do=diff List of abstracts for the workshop Sampling from the Target Distribution * Back to the workshop program * Please click below on a speaker's name to view their abstract. * Schedule: 9H30-10H20 * Title: Learning with Importance Weighted Variational Inference * Joint work$f$$n\geq 1$$q_n$\(\eta \in (0,1 )\)\(q_n\)\(f\)\(\eta \in (0,1 )\)$\eta$$\hat{\pi}_T(f)$$|\hat{\pi}_T − \pi_T(f)| ≤ \varepsilon$$1 − \eta$$f$$O(\log(T\eta^{-1} \varepsilon^{-2}))$$\hat{\pi}_T$ text/html 2025-09-30T13:19:05+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:subworld&rev=1759231145&do=diff Subdirectories ---------- world index ---------- For adding a newpage here, choose the namespace (world, here) and the name of your newpage. ---------- text/html 2022-04-28T14:27:31+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:tennis&rev=1651148851&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2022-03-16T07:40:23+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:totalvariation&rev=1647412823&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2022-11-18T11:14:50+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:useful-bounds&rev=1668766490&do=diff $$ \newcommand{\arginf}{\mathrm{arginf}} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\asconv}[1]{\stackrel{#1-a.s.}{\rightarrow}} \newcommand{\Aset}{\mathsf{A}} \newcommand{\b}[1]{{\mathbf{#1}}} \newcommand{\ball}[1]{\mathsf{B}(#1)} \newcommand{\bbQ}{{\mathbb Q}} \newcommand{\bproof}{\textbf{Proof :}\quad} \newcommand{\bmuf}[2]{b_{#1,#2}} \newcommand{\card}{\mathrm{card}} \newcommand{\chunk}[3]{{#1}_{#2:#3}} \newcommand{\condtrans}[3]{p_{#1}(#2|#3)} \n… text/html 2025-03-11T14:38:22+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:vim-essentiel&rev=1741700302&do=diff Commandes essentielles pour vi L'éditeur `vi` est un éditeur de texte puissant et flexible qui fonctionne en modes différents : le mode commande et le mode insertion. Voici les commandes essentielles pour naviguer, éditer et sauvegarder vos fichiers avec `vi`. text/html 2025-08-01T16:17:51+0200 Anonymous (anonymous@undisclosed.example.com) https://wiki.randaldouc.xyz/doku.php?id=world:visio&rev=1754057871&do=diff Visio 1er aout Syllabus des interventions Indiquez votre disponibilité (tranche horaire) pour une visio le 1er aout ici (double cliquez pour modifier la page (ou sur l'icone de crayon à droite) et n'oubliez pas de cliquer sur save, une fois la page modifiée): * Randal: Dispo toute la journée (8H-18H). Je suis aussi dispo la première semaine d'août.