Random Walks on Supercritical Percolation Clusters
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 C∞in the Euclidean lattice. The bounds, analogous to Aronsen's bounds for uniformly elliptic divergence form diffusions, hold with constan...
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| Veröffentlicht in: | The Annals of probability 2004-10, Vol.32 (4), p.3024-3084 |
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| container_end_page | 3084 |
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| container_title | The Annals of probability |
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| creator | Barlow, Martin T. |
| description | 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 C∞in the Euclidean lattice. The bounds, analogous to Aronsen's bounds for uniformly elliptic divergence form diffusions, hold with constants cidepending 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. |
| doi_str_mv | 10.1214/009117904000000748 |
| format | Article |
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The bounds, analogous to Aronsen's bounds for uniformly elliptic divergence form diffusions, hold with constants cidepending only on p (the percolation probability) and d. 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The bounds, analogous to Aronsen's bounds for uniformly elliptic divergence form diffusions, hold with constants cidepending only on p (the percolation probability) and d. 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| source | JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; EZB-FREE-00999 freely available EZB journals; Project Euclid Complete |
| subjects | 58J35 60K37 Cubes Distribution theory Exact sciences and technology Harmonic functions heat kernel Markov processes Mathematical analysis Mathematical constants Mathematical inequalities Mathematical theorems Mathematics Open star clusters Percolation Probabilities Probability Probability and statistics Probability theory Probability theory and stochastic processes Random walk Random walk theory Sciences and techniques of general use Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications) Stochastic processes Studies Supercritical processes Theorems |
| title | Random Walks on Supercritical Percolation Clusters |
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