This article is cited in 1 paper

Mathematics

Log-Sobolev inequalities on graphs with positive curvature

Y. Lin^a, Sh. Liu^a, H. Song<sup>ab

a</sup> Renmin University of China
^b Beijing International Studies University

Abstract: Based on a global estimate of the heat kernel, some important inequalities such as Poincaré inequality and log-Sobolev inequality, furthermore a tight logarithm Sobolev inequality are presented on graphs, just under a positive curvature condition $CDE'(n,K)$ with some $K>0$. As consequences, we obtain exponential integrability of integrable Lipschitz functions and moment bounds at the same assumption on graphs.

Keywords: Log-Sobolev inequality, Laplacian, $CDE'(n,K)$.

UDC: 517
BBK: 22.161

Language: English

DOI: 10.15688/mpcm.jvolsu.2017.3.8