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].
Citation
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
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