Poincare, modified logarithmic Sobolev and isoperimetric inequalities for Markov chains with non-negative Ricci curvature
Poincare, modified logarithmic Sobolev and isoperimetric inequalities for Markov chains with non-negative Ricci curvature
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DOI：
10.1016/j.jfa.2018.03.011
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发表时间：
2018-06-01
影响因子：
1.7
通讯作者：
Fathi, Max
中科院分区：
文献类型：
--
作者：
Erbar, Matthias;Fathi, Max
研究了离散空间上熵曲率从下有界的马尔可夫链的泛函不等式。我们的主要结果是，当曲率是非负的，但不一定是正的，谱间隙，Cheeger等周常数和链的修正对数Sobolev常数可以由一个常数限定，这个常数只取决于空间的直径，相对于一个合适的度规。这些估计是Li和Yau、Buser和Wang得到的黎曼几何经典结果的离散类似。(C) 2018爱思唯尔公司版权所有。
We study functional inequalities for Markov chains on discrete spaces with entropic Ricci curvature bounded from below. Our main results are that when curvature is non-negative, but not necessarily positive, the spectral gap, the Cheeger isoperimetric constant and the modified logarithmic Sobolev constant of the chain can be bounded from below by a constant that only depends on the diameter of the space, with respect to a suitable metric. These estimates are discrete analogues of classical results of Riemannian geometry obtained by Li and Yau, Buser and Wang. (C) 2018 Elsevier Inc. All rights reserved.