Topic: Markov chains

Entropic independence replaces variance with entropy in an analogue of spectral independence. This talk introduces that property and shows how it can yield sharp bounds on the time required for Markov chains to approach equilibrium.

Localization schemes offer a framework for proving functional inequalities governing Markov chains. This talk introduces the Chen–Eldan approach and shows how local-to-global arguments from high-dimensional expansion fit within it. Examples illustrate the connection and its use in analysing stochastic processes.