Complete logarithmic Sobolev inequalities via Ricci curvature bounded below
Complete logarithmic Sobolev inequalities via Ricci curvature bounded below
复制标题
DOI：
10.1016/j.aim.2021.108129
复制
发表时间：
2022-01-22
影响因子：
1.7
通讯作者：
Junge, Marius
中科院分区：
文献类型：
--
作者：
Brannan, Michael;Gao, Li;Junge, Marius
我们证明了对于对称Markov半群，Ricci曲率由一个非正常数下有界，结合一个有限的L-无穷混合时间，蕴含修正的log-Sobolev不等式.这种L-无穷混合时间估计对于具有谱间隙和有限Varopoulos维数的Markov半群总是成立的。我们的结果适用于最近由Carlen和Maas引入的具有非交换Ricci曲率界的非遍历量子Markov半群。作为应用，我们证明了紧致黎曼流形上的热半群对它的所有矩阵值扩张都存在一个一致修正的log-Sobolev不等式。爱思唯尔公司出版
We prove that for a symmetric Markov semigroup, Ricci curvature bounded from below by a non-positive constant combined with a finite L-infinity-mixing time implies the modified log-Sobolev inequality. Such L-infinity-mixing time estimates always hold for Markov semigroups that have spectral gap and finite Varopoulos dimension. Our results apply to non-ergo dic quantum Markov semigroups with noncommutative Ricci curvature bounds recently introduced by Carlen and Maas. As an application, we prove that the heat semigroup on a compact Riemannian manifold admits a uniform modified log-Sobolev inequality for all its matrix-valued extensions. Published by Elsevier Inc.