Isoperimetry and heat kernel decay on percolation clusters
Probability
2012-09-11 v2
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.
Keywords
Cite
@article{arxiv.math/0301213,
title = {Isoperimetry and heat kernel decay on percolation clusters},
author = {Pierre Mathieu and Elisabeth Remy},
journal= {arXiv preprint arXiv:math/0301213},
year = {2012}
}