Hitting probabilities of random walks on Zd
Hitting probabilities of random walks on Zd
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DOI：
10.1016/0304-4149(87)90196-7
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发表时间：
1987
影响因子：
1.4
通讯作者：
H. Kesten
中科院分区：
文献类型：
--
作者：
H. Kesten
Abstract Let S 0, S 1,… be a simple (nearest neighbor) symmetric random walk on Z d and H B (x, y)= P {S. visits B for the first time at y| S 0= x}. If d= 2 we show that for any connected set B of diameter r, and any y ϵ B, one has lim sup H B (x, y)⩽ C (2) r− 1 2·| x|→∞ If d⩾ 3 one has for any connected set B of cardinality n, lim sup H B (x, y)⩽ C (d) n− 1+ 2 d·| x|→∞ These estimates can be used to give bounds on the maximal growth rate of diffusion limited aggregation, a fashionable growth model for various physical phenomena.
