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2009 Parabolic Harnack inequality and local limit theorem for percolation clusters
Ben Hambly, Martin Barlow
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Electron. J. Probab. 14: 1-26 (2009). DOI: 10.1214/EJP.v14-587


We consider the random walk on supercritical percolation clusters in $\mathbb{Z}^d$. 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.


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Ben Hambly. Martin Barlow. "Parabolic Harnack inequality and local limit theorem for percolation clusters." Electron. J. Probab. 14 1 - 26, 2009.


Accepted: 7 January 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1192.60107
MathSciNet: MR2471657
Digital Object Identifier: 10.1214/EJP.v14-587

Primary: 60G50
Secondary: 31B05

Keywords: Harnack inequality , local limit theorem , percolation , Random walk

Vol.14 • 2009
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