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February, 1991 Geometric Bounds for Eigenvalues of Markov Chains
Persi Diaconis, Daniel Stroock
Ann. Appl. Probab. 1(1): 36-61 (February, 1991). DOI: 10.1214/aoap/1177005980

Abstract

We develop bounds for the second largest eigenvalue and spectral gap of a reversible Markov chain. The bounds depend on geometric quantities such as the maximum degree, diameter and covering number of associated graphs. The bounds compare well with exact answers for a variety of simple chains and seem better than bounds derived through Cheeger-like inequalities. They offer improved rates of convergence for the random walk associated to approximate computation of the permanent.

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Persi Diaconis. Daniel Stroock. "Geometric Bounds for Eigenvalues of Markov Chains." Ann. Appl. Probab. 1 (1) 36 - 61, February, 1991. https://doi.org/10.1214/aoap/1177005980

Information

Published: February, 1991
First available in Project Euclid: 19 April 2007

zbMATH: 0731.60061
MathSciNet: MR1097463
Digital Object Identifier: 10.1214/aoap/1177005980

Subjects:
Primary: 60J10
Secondary: 60C05

Keywords: Eigenvalues , Markov chains , Random walk

Rights: Copyright © 1991 Institute of Mathematical Statistics

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Vol.1 • No. 1 • February, 1991
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