Bibliography: An introduction to Markov Processes, second edition, Springer, by Daniel Stroock Markov Chains and Mixing times, AMS, by David Levin, Yuval Peres and E. Wilmer.

Problem set 1, due Thursday, February 20

Problem set 2, due Thursday, February 27

Problem set 3, due Thursday, March 13

Problem set 4, due Thursday, March 20

Problem set 5, due Thursday, April 3

Problem set 6, due Thursday, April 10

Problem set 7, due Thursday, April 24

Problem set 8 (and last), due Thursday, May 8 We will follow Stroock book up to chapter 5, and end the course with some elements of chapter 6 and/or of Levin-Peres-Wilmer book. Program: --February: -02/4--02/6: Section 1.1 of Stroock book (recurrence/transience of random walk on Z). -02/11--02/13: Section 1.2 (random walk on /transience of random walk on Z^d). Random walk on finite sets. Beginning of Chapter 2: definition of Markov chains in a discrete state space/discrete time. -02/18--02/20: Doeblin theory. -02/25--02/27: Return times and the stationnary measure (end of chapter 2), Classification of states, criteria, stationary probabilities (beginning chapter 3) -03/04--03/06: Classification of states, criteria, aperiodicity -03/11--03/13: aperiodicity, stationary probabilities, Wilson algorithm (end of chapter 3) -03/18--03/20: End of Wilson algorithm (end of chapter 3 of Stroock book), Coupling techniques: Chapter 4 and beginning of chapter 5 in Levin-Peres-Wilmer's book. -03/31--04/03: Coupling and strong stationary times, end of chapter 5 and chapter 6 in Levin-Peres-Wilmer's book. -04/08--04/10: end of chapter 6 and chapter 7 in Levin-Peres-Wilmer's book. 04/15--04/17:Mixing in Expander graphs (chapter 12-13 in Levin-Peres-Wilmer), beginning of chapter 4 in Stroock book. . 04/24:end of chapter 4 in Stroock book. -04/28--05/01: Chapter 5 in Stroock book