### An asymptotically optimal mixing-time bound on the bases-exchange Markov chain for a matroid

Probability Seminar

21st April 2023, 3:30 pm – 4:30 pm

Fry Building, 2.04

We discuss our results on the problem of sampling bases of a matroid. In particular, we will discuss a modified log-Sobolev inequality for r-homogeneous strongly log-concave distributions. As a consequence, we obtain an asymptotically optimal mixing time bound for the bases-exchange chain and a concentration result for such distributions. I will also mention some continuing results by other authors, which extended this work

Joint work with Heng Guo and Giorgos Mousa.

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