Lin Y., Liu S., Song H. Log-Sobolev Inequalities on Graphs With Positive Curvature

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https://doi.org/10.15688/mpcm.jvolsu.2017.3.8

Yong Lin
Professor, Department of Mathematics,
Renmin University of China
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59 Zhongguancun Street, Haidian District Beijing, 100872, P.R. China

Shuang Liu
Student, Department of Mathematics,
Renmin University of China
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59 Zhongguancun Street, Haidian District Beijing, 100872, P.R. China

Hongye Song
Lecturer, Department of Mathematics, Renmin University of China,
59 Zhongguancun Street, Haidian District Beijing, 100872, P.R. China
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Beijing International Studies University,
1 Dingfuzhuang Nanli, Chaoyang District, Beijing, China

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.

Key words: Log-Sobolev inequality, Laplacian, CDE′ (n, K) .

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Log-Sobolev Inequalities on Graphs With Positive Curvature by Lin Y., Liu S., Song H. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Mathematical Physics and Computer Simulation. №3 (40) 2017 pp. 99-110

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