Markov chain curvature and mixing

Orateur:
Florentin MUNCH
Localisation: Institut Max-Planck de Leipzig, Allemagne
Type: Groupe de travail Convexité, Transport Optimal et Probabilités (CTOP)
Site: Hors LAMA , IHP
Date de début:
25/04/2024 - 14:00
Date de fin:
25/04/2024 - 17:00

We show that the Ollivier Ricci curvature of a Markov chain controls the log-Sobolev constant. In case of non-negative Ollivier sectional curvature, the log-Sobolev constant can be lower bounded by the minimum Ollivier Ricci curvature. By this, we answer an open question by Peres and Tetali. In case of non-negative Ricci curvature, the log-Sobolev constant can be lower bounded in terms of the diameter. Moreover in case of non-negative Ollivier Ricci curvature, we give an upper bound for the spectral gap in terms of the mixing time. This gives a quantitative negative answer to the question by Naor and Milman, whether there can be expander graphs with non-negative curvature.