| | Prof | Chapters | Topics | Material | Cours |
| 1 | (AD) | Chapt. 1 and 2. | Introduction to Markov chains, first definitions, Markov kernel, Elementary operations. Invariant measures / reversibility | Exercise sheet 1 | 1 |
| 2 | (AD) | Chapt. 2 and 3 | Canonical space. Kolmogorov extension theorem. Strong Markov property.Applications of the Markov properties: Stopping times. | Exercise sheet 2 | 2 |
| 3 | (AD) | | Dynamical systems, Birkhoff theorem | | |
| 4 | (AD) | Chapt. 3 | Metrics: TV norms, V norms, Wasserstein. | Exercise sheet 3 | 3 |
| Oct. 31 | (RD) | Chap 5 | Geometric ergodicity. | Chapitre 3 de ce polycopié | 4/5 |
| Nov 14 | (RD) | Chapt. 6 | Central Limit Theorems | | 6 |
| Nov 21 | (RD) | Chap 6 | Rosenthal inequalities (Alain). | | 7 |
| Nov 28 | (AD) | Chapt. 6-7-8 | Quantitative Central Limit theorems | | 8 |
| Dec 5 | (RD) | Chapt. 18-19 | Convergence via spectral methods | | 9 |
| Dec 12 | (AD) | Chap 21 | Contractive convergence via curvature lower bounds. | | 10 |