L∞-OPTIMAL TRANSPORT OF ANISOTROPIC LOG-CONCAVE MEASURES AND EXPONENTIAL CONVERGENCE IN FISHER'S INFINITESIMAL MODEL
成果类型：
Article
署名作者：
Khudiakova, Ksenia A.; Maas, Jan; Pedrotti, Francesco
署名单位：
Institute of Science & Technology - Austria
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/25-AAP2162
发表日期：
2025
页码：
1913-1940
关键词：
摘要：
We prove upper bounds on the L infinity-Wasserstein distance from optimal transport between strongly log-concave probability densities and logLipschitz perturbations. In the simplest setting, such a bound amounts to a transport-information inequality involving the L infinity-Wasserstein metric and the relative L infinity-Fisher information. We show that this inequality can be sharpened significantly in situations where the involved densities are anisotropic. Our proof is based on probabilistic techniques using Langevin dynamics. As an application of these results, we obtain sharp exponential rates of convergence in Fisher's infinitesimal model from quantitative genetics, generalising recent results by Calvez, Poyato, and Santambrogio in dimension 1 to arbitrary dimensions.