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

Details
Hits: 920

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

Yong Lin
Professor, Department of Mathematics,
Renmin University of China
This email address is being protected from spambots. You need JavaScript enabled to view it.
59 Zhongguancun Street, Haidian District Beijing, 100872, P.R. China

Shuang Liu
Student, Department of Mathematics,
Renmin University of China
This email address is being protected from spambots. You need JavaScript enabled to view it.
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
This email address is being protected from spambots. You need JavaScript enabled to view it.
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) .

Creative Commons License

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

Attachments:
Download this file (Lin_i_dr.pdf) Lin_i_dr.pdf
URL: https://mp.jvolsu.com/index.php/en/component/attachments/download/710		1163 Downloads