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Parabolic Harnack inequality and local limit theorem for percolation clusters

   
@article{EJP587,
	author = {Ben Hambly and Martin Barlow},
	title = {Parabolic Harnack inequality and local limit theorem for percolation clusters},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {14},
	year = {2009},
	keywords = {Percolation; random walk; Harnack inequality; local limit theorem},
	abstract = {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.},
	pages = {no. 1, 1-26},
	issn = {1083-6489},
	doi = {10.1214/EJP.v14-587},    
        url = {http://ejp.ejpecp.org/article/view/587}}