Organized by:
- Evita Nestoridi ( Stony Brook University)
- Dominik Schmid ( Bonn University)
Markov chains serve as indispensable tools for generating random structures, such as graph colorings, vector space bases, and polygon triangulations. Mixing times capture the temporal evolution towards equilibrium. Of particular interest is the abrupt transition from unmixed to mixed – the cutoff phenomenon. The cutoff phenomenon was first discovered by Diaconis and Shashahani in the context of card shuffling. Many techniques from representation theory, combinatorics and probability, comparison theory, Nash inequalities, evolving sets, distinguishing statistics, and many more have been developed to understand mixing times. The question whether cutoff occurs was solved over the years for many models, for example random walks on random graphs, the card shuffles, or the east process. In recent years, many new techniques to verify the occurrence or absence of cutoff, as well as even more refined results on the convergence towards the stationary distribution, were established.
Our main goal is to bring together people with backgrounds from mathematical physics, probability theory and theoretical computer science, and develop new insights on mixing times. In particular, the interplay between the exciting new methods from recent years including information percolation, stochastic localization, and varentropy methods is promising towards improving the understanding of cutoff. Another goal is to strengthen the research on limit profiles, which are an exciting new objective in the study of mixing times for Markov chains.
