Random walks on supercritical percolation clusters

• 成果类型: Article
• 署名作者: Barlow, MT
• 署名单位: University of British Columbia
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000000748
• 发表日期: 2004
• 页码: 3024-3084
• 关键词: parabolic harnack inequality; order large deviations; sierpinski carpet; infinite cluster; brownian-motion; heat kernels; upper-bounds; graphs

摘要

We obtain Gaussian upper and lower bounds on the transition density q(t)(x, y) of the continuous time simple random walk on a supercritical percolation cluster C(infinity) in the Euclidean lattice. The bounds, analogous to Aronsen's bounds for uniformly elliptic divergence form diffusions, hold with constants c(i) depending only on p (the percolation probability) and d. The irregular nature of the medium means that the bound for q(t) (x, (.)) holds only for t greater than or equal to S(x) (omega), where the constant S(x) (omega) depends on the percolation configuration omega.