Measured expanders

IF 0.5 3区数学 Q3 MATHEMATICS

Journal of Topology and Analysis Pub Date : 2021-04-13 DOI:10.1142/s1793525322500078

Kang Li, Ján Špakula, Jiawen Zhang

引用次数: 1

Abstract

By measured graphs, we mean graphs endowed with a measure on the set of vertices. In this context, we explore the relations between the appropriate Cheeger constant and Poincaré inequalities. We prove that the so-called Cheeger inequality holds in two cases: when the measure comes from a random walk, or when the measure has a bounded measure ratio. Moreover, we also prove that our measured (asymptotic) expanders are generalised expanders introduced by Tessera. Finally, we present some examples to demonstrate relations and differences between classical expander graphs and the measured ones. This paper is motivated primarily by our previous work on the rigidity problem for Roe algebras.

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测量扩展器

所谓测量图，是指在顶点集合上被赋值的图。在这种情况下，我们探讨了适当的Cheeger常数和poincarcarr不等式之间的关系。我们证明了所谓的Cheeger不等式在两种情况下成立:当测度来自随机游走时，或者当测度具有有界测度比时。此外，我们还证明了我们的可测(渐近)膨胀子是由Tessera引入的广义膨胀子。最后，通过实例说明了经典展开图与实测展开图之间的联系和区别。本文的动机主要是由我们以前的工作对罗伊代数的刚性问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Topology and Analysis MATHEMATICS-

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is devoted to topology and analysis, broadly defined to include, for instance, differential geometry, geometric topology, geometric analysis, geometric group theory, index theory, noncommutative geometry, and aspects of probability on discrete structures, and geometry of Banach spaces. We welcome all excellent papers that have a geometric and/or analytic flavor that fosters the interactions between these fields. Papers published in this journal should break new ground or represent definitive progress on problems of current interest. On rare occasion, we will also accept survey papers.