On nodal domains and higher-order Cheeger inequalities of finite reversible Markov processes
type: Item
instance of: scholarly article
title: On nodal domains and higher-order Cheeger inequalities of finite reversible Markov processes
zbMATH Open document ID: 1260.60153
author: Amir Daneshgar
author: Ramin Javadi
author: Laurent Miclo
published in: Stochastic Processes and their Applications
publication date: 2012-06-01T00:00:00Z
reviewed by: Sophia L. Kalpazidou
Mathematics Subject Classification ID: 60J27
Mathematics Subject Classification ID: 60J35
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 31C20
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05C80
zbMATH DE Number: 6040302
zbMATH Keywords: reversible Markovian generator
zbMATH Keywords: Cheeger's inequality
MaRDI profile type: Publication
full work available at URL: j.spa.2012.02.009
OpenAlex ID: W2154656691
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DOI: 10.1016/J.SPA.2012.02.009
review text: Classical Cheeger inequalities for finite reversible Markov processes make a link between the spectral gap and the connectivity constants, which are obtained by minimizing isoperimetric-type quotients over decompositions of the state space into two disjoint parts. The purpose of the paper is to obtain such inequalities between the whole spectrum and decompositions of the state space into several parts, when the underlying graph is a cycle.NEWLINENEWLINE Furthermore, the relation between an intermediate Dirichlet connectivity spectrum and the nodal domains of the eigenfunctions of the finite reversible Markov process under consideration is investigated.
description: scientific article; zbMATH DE number 6040302