Welcome to Randal Douc's wiki

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====== A course on Markov Chains: Advanced topics ======
  * **Trick:** The real address of this page is: <color /yellow>https://wiki.randaldouc.xyz/doku.php?id=world:markovchains</color> but there is also an equivalent (more simple) address: https://lstu.fr/markovchains

====== Registration to the course ======
 
  * <color /yellow> [[https://docs.google.com/forms/d/e/1FAIpQLSdjk1HhX6lfoIpbrT7aWqFPoZcpwtp4aSwMxw2PxM55MgVtnA/viewform?usp=sf_link|Please register here]] </color>

====== Program of the course ======
  * **Where?** Institut de Mathématiques d'ORSAY. Room: 1A14. 
  * **When?** Every course will hold on Thursday <color red>from 9H to 12H00</color> (exact dates are given below). 
  * **Who?** The list of the teachers are given below with their acronyms: 
    * AD: Alain Durmus. 
    * RD: Randal Douc.
  * **What?** The chapters refer to the book: [[https://www.springer.com/gp/book/9783319977034|Markov chains]] by R. Douc, E. Moulines, P. Priouret and P. Soulier. Springer publishers. 
  * **Teaching material**:  {{world:mainmc-tome1.pdf|pdf version of Markov Chains book}}
 
^           ^ Prof  ^ Chapters         ^ Topics                                                                                                         ^ Material                                              ^ Cours  ^
| Sept. 26  | (AD)  | Chapt. 1 and 2.  | Introduction to Markov chains                                                             | {{:world:ex1.pdf| Exercise sheet 1}}                                                      | 1      |
| Oct. 3    | (AD)  | Chapt. 2 and 3   | Invariance, Reversibility. MCMC. Canonical space.                                  |  {{:world:ex_2_2024.pdf| Exercise sheet 2}}            | 2      |
| Oct. 17   |       |                  | Pause                                                                                                          |                                                       |        |
| Oct. 24   | (AD)  | Chapt. 3         | Canonical space (end). Stopping time, (Strong) Markov property, Harmonic functions, martingales  | {{:world:ex_3_2024.pdf| Exercise sheet 3}}                                                      | 3      |
| Oct. 31  | (AD)  | Chap 5           | Ergodic theory.                                                                 |                                                       | 4      |
| Oct 31    | (AD)  | Chapt  5         | Drift functions. Maximum principle, Solidarity property. Comparison theorem. Atomic chains (atoms, recurrence, transience).                                                                                      |                                                       | 5      |
| Nov 7     | (RD)  | Chapt. 8         | Atomic chains (continued)                                                                         | Chapitre 3 de ce {{ :world:polymcmc.pdf |polycopié}}  | 6      |
| Nov 14    | (RD)  | Chap  9          | Renewal theory, Kac's theorem                                                                                  |                                                       | 7      |
| Nov 21    | (RD)  | Chapt. 9         | Blackwell's and Kendall's theorem                                                                              |                                                       | 9      |
| Nov 28    | (RD)  | Chapt. 19        | Coupling methods, small sets and geometric ergodicity                                                          | {{ :world:polymcmc.pdf |polycopié}}                   | 10     |
| Dec 2     | (RD)  | Chap 19          | End of geometric ergodicity. Revision's exercises.                                                             |                                                       |        |

===== Example of an examination =====
  * {{ :world:controle.pdf |An examination given in 2019-2020}}
  * {{ :world:controleCorrige.pdf |Solution of the examination given in 2019-2020}}

===== Projects =====
  * <fc #ff0000>A short summary (5 pages max) of the paper</fc> is requested before the defense by sending an email to Alain Durmus. You can add technical appendix (with no limitation size).
  * The <fc #ff0000>defense will be 20 minutes</fc> long per project + questions. Be as pedagogical as possible, you can highlight a particular proof that interests you if you find it interesting.
  * Please read the <color /yellow>{{ :world:guidelinesmda.pdf |guidelines for the report}}</color>.    
  * If there is any question, please contact Alain Durmus.

/* ===== Evaluation =====

**Evaluation**: The exam will take place on Thursday, December 16, 2021. It is a 3-hour table-top assignment [all documents are allowed]. 
*/
===== Contact =====

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