Which values of the volume growth and escape time exponent are possible for a graph?
type: Item
instance of: scholarly article
title: Which values of the volume growth and escape time exponent are possible for a graph?
zbMATH Open document ID: 1051.60071
DOI: 10.4171/RMI/378
author: Martin T. Barlow
published in: Revista Matemática Iberoamericana
publication date: 2004-09-28T00:00:00Z
full work available at URL: https://eudml.org/doc/39628
review text: Many mathematical questions pertaining to heat kernels on manifolds can be posed with respect to locally finite weighted graphs on measurable spaces, where the level of technical difficulties is lower, but the same basic principles apply. Typically, one relates geometric properties, like e.g. the graph distance, Ahlfors regularity or volume doubling (those are encoded in the one-parameter family of volume growth functions \(V_{\alpha }\)), and analytic ones (e.g. Sobolev and Harnack inequalities) with global properties of the random walk and its transition density. In the present paper, conditions are established for the numerical range of two exponents: \(\alpha \) in the Ahlfors regularity condition and \(\beta \) in the escape time exponent for random walks (and continuous time random walks) on infinite weighted graphs.
reviewed by: Piotr Garbaczewski
Mathematics Subject Classification ID: 60J05
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 82C41
zbMATH DE Number: 2104136
zbMATH Keywords: graph
zbMATH Keywords: random walk
zbMATH Keywords: volume growth
zbMATH Keywords: elliptic Harnack inequality
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2104136