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February 1999 Comparing eigenvalue bounds for Markov chains: when does Poincaré beat Cheeger?
Jason Fulman, Elizabeth L. Wilmer
Ann. Appl. Probab. 9(1): 1-13 (February 1999). DOI: 10.1214/aoap/1029962594


The Poincaré and Cheeger bounds are two useful bounds for the second largest eigenvalue of a reversible Markov chain. Diaconis and Stroock and Jerrum and Sinclair develop versions of these bounds which involve choosing paths. This paper studies these path-related bounds and shows that the Poincaré bound is superior to the Cheeger bound for simple random walk on a tree and random walk on a finite group with any symmetric generating set. This partially resolves a question posed by Diaconis and Stroock.


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Jason Fulman. Elizabeth L. Wilmer. "Comparing eigenvalue bounds for Markov chains: when does Poincaré beat Cheeger?." Ann. Appl. Probab. 9 (1) 1 - 13, February 1999.


Published: February 1999
First available in Project Euclid: 21 August 2002

zbMATH: 0935.60057
MathSciNet: MR1682369
Digital Object Identifier: 10.1214/aoap/1029962594

Primary: 60C05 , 60J10

Keywords: Cheeger inequalitites , Eigenvalues , groups , Markov chains , Poincaré inequalities , Random walk , trees

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.9 • No. 1 • February 1999
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