Logarithmic Sobolev, isoperimetry and transport inequalities on graphs

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• 作者：Yu Tao Ma ; Ran Wang ; Li Ming Wu
• 关键词：Graph ; log ; Sobolev inequality ; isoperimetry ; transport inequality
• 刊名：Acta Mathematica Sinica
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：32
• 期：10
• 页码：1221-1236
• 全文大小：252 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Chinese Library of Science
  
• 出版者：Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society, co-published
• ISSN：1439-7617
• 卷排序：32

文摘

In this paper, we study some functional inequalities (such as Poincaré inequality, logarithmic Sobolev inequality, generalized Cheeger isoperimetric inequality, transportation-information inequality and transportation-entropy inequality) for reversible nearest-neighbor Markov processes on connected finite graphs by means of (random) path method. We provide estimates of the involved constants.