This mini-course will present the fundamentals of analysis of convergence rates of discrete time Markov chains, and applications from statistical physics and combinatorics. It will start with an introduction to Markov chains and their properties, and relation between sampling and counting. Then it will discuss techniques for bounding the mixing time: The second session will focus on coupling and the third session on canonical paths and related concepts.

The second session of this mini course will take place on Tuesday, January 26 from 9:30 am – 10:30 am; the third session of this mini course will take place on Wednesday, January 27 from 3:00 pm – 4:00 pm.