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April, 1993 Gaussian Estimates for Markov Chains and Random Walks on Groups
W. Hebisch, L. Saloff-Coste
Ann. Probab. 21(2): 673-709 (April, 1993). DOI: 10.1214/aop/1176989263

Abstract

A Gaussian upper bound for the iterated kernels of Markov chains is obtained under some natural conditions. This result applies in particular to simple random walks on any locally compact unimodular group $G$ which is compactly generated. Moreover, if $G$ has polynomial volume growth, the Gaussian upper bound can be complemented with a similar lower bound. Various applications are presented. In the process, we offer a new proof of Varopoulos' results relating the uniform decay of convolution powers to the volume growth of $G$.

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W. Hebisch. L. Saloff-Coste. "Gaussian Estimates for Markov Chains and Random Walks on Groups." Ann. Probab. 21 (2) 673 - 709, April, 1993. https://doi.org/10.1214/aop/1176989263

Information

Published: April, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0776.60086
MathSciNet: MR1217561
Digital Object Identifier: 10.1214/aop/1176989263

Subjects:
Primary: 60J15
Secondary: 60B15

Keywords: convolution , Gaussian estimates , groups , Markov chain , Random walk

Rights: Copyright © 1993 Institute of Mathematical Statistics

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Vol.21 • No. 2 • April, 1993
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