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January 2004 Isoperimetry and heat kernel decay on percolation clusters
Pierre Mathieu, Elisabeth Remy
Ann. Probab. 32(1A): 100-128 (January 2004). DOI: 10.1214/aop/1078415830

Abstract

We prove that the heat kernel on the infinite Bernoulli percolation cluster in $\Z^d$ almost surely decays faster than $t^{-d/2}$. We also derive estimates on the mixing time for the random walk confined to a finite box. Our approach is based on local isoperimetric inequalities. Some of the results of this paper were previously announced in the note of Mathieu and Remy [C. R. Acad. Sci. Paris Sér. I Math. 332 (2001) 927--931].

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Pierre Mathieu. Elisabeth Remy. "Isoperimetry and heat kernel decay on percolation clusters." Ann. Probab. 32 (1A) 100 - 128, January 2004. https://doi.org/10.1214/aop/1078415830

Information

Published: January 2004
First available in Project Euclid: 4 March 2004

zbMATH: 1078.60085
MathSciNet: MR2040777
Digital Object Identifier: 10.1214/aop/1078415830

Subjects:
Primary: 60D05, 60J10

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.32 • No. 1A • January 2004
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