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 Electronic Journal of Probability > Vol. 14 (2009) > Paper 1 open journal systems 


Parabolic Harnack inequality and local limit theorem for percolation clusters

Ben M Hambly, University of Oxford
Martin T Barlow, University of British Columbia


Abstract
We consider the random walk on supercritical percolation clusters in Zd. Previous papers have obtained Gaussian heat kernel bounds, and a.s. invariance principles for this process. We show how this information leads to a parabolic Harnack inequality, a local limit theorem and estimates on the Green's function.


Full text: PDF

Pages: 1-26

Published on: January 7, 2009
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Electronic Journal of Probability. ISSN: 1083-6489