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Log-Sobolev Inequalities on Graphs with Positive Curvature

Yong Lin Department of Mathematics, Renmin University of China Shuang Liu Department of Mathematics, Renmin University of China Hongye Song Department of Mathematics, Renmin University of China; Beijing International Studies University

Analysis of PDEs mathscidoc:2207.03004

Mathematical Physics and Computer Simulation, 20, (3), 99-110, 2017.9
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.
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@inproceedings{yong2017log-sobolev,
  title={Log-Sobolev Inequalities on Graphs with Positive Curvature},
  author={Yong Lin, Shuang Liu, and Hongye Song},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707122836485614561},
  booktitle={Mathematical Physics and Computer Simulation},
  volume={20},
  number={3},
  pages={99-110},
  year={2017},
}
Yong Lin, Shuang Liu, and Hongye Song. Log-Sobolev Inequalities on Graphs with Positive Curvature. 2017. Vol. 20. In Mathematical Physics and Computer Simulation. pp.99-110. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707122836485614561.
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