Geodesic
Log-Sobolev inequalities on graphs with positive curvature
Matematičeskaâ fizika i kompʹûternoe modelirovanie, Tome 20 (2017) no. 3, pp. 99-110

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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
Mots-clés : $CDE'(n,K)$. 
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     author = {Y. Lin and Sh. Liu and H. Song},
     title = {Log-Sobolev inequalities on graphs with positive curvature},
     journal = {Matemati\v{c}eska\^a fizika i kompʹ\^uternoe modelirovanie},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VVGUM_2017_20_3_a8/}
}
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Y. Lin; Sh. Liu; H. Song. Log-Sobolev inequalities on graphs with positive curvature. Matematičeskaâ fizika i kompʹûternoe modelirovanie, Tome 20 (2017) no. 3, pp. 99-110. http://geodesic.mathdoc.fr/item/VVGUM_2017_20_3_a8/