Hitting probabilities of random walks on

Harry Kesten

Stochastic Processes and their Applications, 1987, vol. 25, 165-184

Abstract: Let S0, S1, ... be a simple (nearest neighbor) symmetric random walk on and HB(x,y) = P{S. visits B for the first time at yS0 = x}. If d = 2 we show that for any connected set B of diameter r, and any y [epsilon] B, one has lim sup HB(x, y) [less-than-or-equals, slant] C(2) r-1/2 · x --> [infinity] If d [greater-or-equal, slanted] 3 one has for any connected set B of cardinality n, lim sup HB(x, y) [less-than-or-equals, slant] C(d)n-1+2/d · x --> [infinity] 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.

Keywords: random; walk; hitting; probabilities; diffusion; limited; aggregation; harmonic; measure (search for similar items in EconPapers)
Date: 1987
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Citations: View citations in EconPapers (3)

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