Lin Y., Liu S., Song H. Log-Sobolev Inequalities on Graphs With Positive Curvature
- Details
- Hits: 973
https://doi.org/10.15688/mpcm.jvolsu.2017.3.8
Yong Lin
Professor, Department of Mathematics,
Renmin University of China
linyong01@ruc.edu.cn
59 Zhongguancun Street, Haidian District Beijing, 100872, P.R. China
Shuang Liu
Student, Department of Mathematics,
Renmin University of China
cherrybu@ruc.edu.cn
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
songhongye@bisu.edu.cn
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) .
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
 Lin_i_dr.pdfURL: https://mp.jvolsu.com/index.php/en/component/attachments/download/710 | 1199 Downloads |