The Annals of Probability
- Ann. Probab.
- Volume 32, Number 4 (2004), 3024-3084.
Random walks on supercritical percolation clusters
Full-text: Open access
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 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 t≥Sx(ω), where the constant Sx(ω) depends on the percolation configuration ω.
Article information
Source
Ann. Probab., Volume 32, Number 4 (2004), 3024-3084.
Dates
First available in Project Euclid: 8 February 2005
Permanent link to this document
https://projecteuclid.org/euclid.aop/1107883346
Digital Object Identifier
doi:10.1214/009117904000000748
Mathematical Reviews number (MathSciNet)
MR2094438
Zentralblatt MATH identifier
1067.60101
Subjects
Primary: 60K37: Processes in random environments
Secondary: 58J35: Heat and other parabolic equation methods
Keywords
Percolation random walk heat kernel
Citation
Barlow, Martin T. Random walks on supercritical percolation clusters. Ann. Probab. 32 (2004), no. 4, 3024--3084. doi:10.1214/009117904000000748. https://projecteuclid.org/euclid.aop/1107883346
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