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Stochastics and Statistics Seminar Series

Regularized modified log-Sobolev inequalities, and comparison of Markov chains

September 30, 2022 @ 11:00 am - 12:00 pm

Konstantin Tikhomirov, Georgia Institute of Technology


Abstract: In this work, we develop a comparison procedure for the Modified log-Sobolev Inequality (MLSI) constants of two reversible Markov chains on a finite state space. As an application, we provide a sharp estimate of the MLSI constant of the switch chain on the set of simple bipartite regular graphs of size n with a fixed degree d. Our estimate implies that the total variation mixing time of the switch chain is of order O(n log(n)). The result is optimal up to a multiple depending on d and resolves an old open problem. Based on joint work with Pierre Youssef.

Konstantin Tikhomirov is an Assistant Professor at the School of Mathematics at the Georgia Institute of Technology, with interests in discrete probability, combinatorics, convex geometry, and applications to data analysis.

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