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October 2004 Random walks on supercritical percolation clusters
Martin T. Barlow
Ann. Probab. 32(4): 3024-3084 (October 2004). DOI: 10.1214/009117904000000748

Abstract

We obtain Gaussian upper and lower bounds on the transition density qt(x,y) of the continuous time simple random walk on a supercritical percolation cluster ${\mathcal{C}}_{\infty}$ in the Euclidean lattice. The bounds, analogous to Aronsen’s bounds for uniformly elliptic divergence form diffusions, hold with constants ci depending only on p (the percolation probability) and d. The irregular nature of the medium means that the bound for qt(x,⋅) holds only for tSx(ω), where the constant Sx(ω) depends on the percolation configuration ω.

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Martin T. Barlow. "Random walks on supercritical percolation clusters." Ann. Probab. 32 (4) 3024 - 3084, October 2004. https://doi.org/10.1214/009117904000000748

Information

Published: October 2004
First available in Project Euclid: 8 February 2005

zbMATH: 1067.60101
MathSciNet: MR2094438
Digital Object Identifier: 10.1214/009117904000000748

Subjects:
Primary: 60K37
Secondary: 58J35

Keywords: heat kernel , percolation , Random walk

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.32 • No. 4 • October 2004
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