论文信息 - Isoperimetry and heat kernel decay on percolation clusters

Isoperimetry and heat kernel decay on percolation clusters

We prove that the heat kernel on the infinite Bernoulli percolation cluster in \Zd 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 Ser. I Math. 332 (2001) 927--931].

É. Remy | P. Mathieu

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