Entropy and curvature of Markov chains: beyond the Peres-Tetali conjecture

Justin SALEZ, Université Paris Dauphine

This talk is devoted to the recently discovered relation between the Ollivier-Ricci curvature of a Markov chain and the entropy decay of the associated semi-group. After a brief introduction to those fundamental notions, I will state our main result and illustrate it with several applications, including exclusion processes, permutation walks, Gibbs samplers for high-temperature spin systems, and attractive zero-range dynamics. Joint work with Pietro Caputo and Florentin Münch.

Area: IS18 - Mixing times (Federico Sau)

Keywords: Markov Chain, Curvature, Peres-Tetali conjecture

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