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January 2000 Cheeger's inequalities for general symmetric forms and existence criteria for spectral gap
Mu-Fa Chen, Feng-Yu Wang
Ann. Probab. 28(1): 235-257 (January 2000). DOI: 10.1214/aop/1019160118

Abstract

In this paper, some new forms of Cheeger’s inequalities are established for general (maybe unbounded) symmetric forms (Theorems 1.1 and 1.2): the resulting estimates improve and extend the ones obtained by Lawler and Sokal for bounded jump processes. Furthermore, some existence criteria for spectral gap of general symmetric forms or general reversible Markov processes are presented (Theorems 1.4 and 3.1), based on Cheeger’s inequalities and a relationship between the spectral gap and the first Dirichlet and Neumann eigenvalues on local region.

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Mu-Fa Chen. Feng-Yu Wang. "Cheeger's inequalities for general symmetric forms and existence criteria for spectral gap." Ann. Probab. 28 (1) 235 - 257, January 2000. https://doi.org/10.1214/aop/1019160118

Information

Published: January 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1044.60078
MathSciNet: MR1756004
Digital Object Identifier: 10.1214/aop/1019160118

Subjects:
Primary: 47A75 , 60J25 , 60J75

Keywords: Cheeger’s inequality , jump process , Neumann and Dirichlet eigenvalue , spectral gap

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 1 • January 2000
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