From the 1 of 7 linked papers with an AI index.
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The local product condition implies cutoff
Francesco Pedrotti, Justin Salez
In the theory of mixing times, a famously wrong conjecture predicts that a sequence of Markov processes exhibits cutoff as soon as the product of their Poincaré constant and mixin…
Entropy-Wasserstein regularization, defective local concentration and a cutoff criterion beyond non-negative curvature
Francesco Pedrotti
Notions of positive curvature have been shown to imply many remarkable properties for Markov processes, in terms, e.g., of regularization effects, functional inequalities, mixing t…
A transport approach to the cutoff phenomenon
Francesco Pedrotti, Justin Salez
Substantial progress has recently been made in the understanding of the cutoff phenomenon for Markov processes, using an information-theoretic statistics known as varentropy [Sal23…
-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher's infinitesimal model
Ksenia A. Khudiakova, Jan Maas, Francesco Pedrotti
We prove upper bounds on the -Wasserstein distance from optimal transport between strongly log-concave probability densities and log-Lipschitz perturbations. In the simpl…
Contractive coupling rates and curvature lower bounds for Markov chains
Francesco Pedrotti
Contractive coupling rates have been recently introduced by Conforti as a tool to establish convex Sobolev inequalities (including modified log-Sobolev and Poincaré inequality) fo…
A new cutoff criterion for non-negatively curved chains
Francesco Pedrotti, Justin Salez
The cutoff phenomenon was recently shown to systematically follow from non-negative curvature and the product condition, for all Markov diffusions. The proof crucially relied on a…