Mixing time bounds, cutoff and limit profiles for Markov chains

Evita Nestoridi

In this mini course, I will discuss various techniques and ideas for bounding mixing times of Markov chains. The main focus will be on proving sharp bounds leading to the existence of cutoff (with optimal window) and, sometimes, to a description of the limit profile. I will present several applications coming from statistical mechanics, card shuffling, graph theory, statistics, and computer science.