Isoperimetry and heat kernel decay on percolation clusters

Details Isoperimetry and heat kernel decay on percolation clusters Isoperimetry and heat kernel decay on percolation clusters

2003-01-20

arxiv.org/abs/math/0301213v2

Mathematics

Probability

Scientific paper

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.

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