Isoperimetry and heat kernel decay on percolation clusters

Pierre Mathieu, Elisabeth Remy

Published 2003-01-20, updated 2003-03-19Version 2

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.