Martin Capacity for Markov Chains

Details Martin Capacity for Markov Chains Martin Capacity for Markov Chains

2004-04-02

arxiv.org/abs/math/0404054v1

Ann. Probab., 23, 1332 - 1346 (1995)

Mathematics

Probability

21 pages

Scientific paper

The probability that a transient Markov chain, or a Brownian path, will ever visit a given set Lambda, is classically estimated using the capacity of Lambda with respect to the Green kernel G(x,y). We show that replacing the Green kernel by the Martin kernel G(x,y)/G(0,y) yields improved estimates, which are exact up to a factor of 2. These estimates are applied to random walks on lattices, and also to explain a connection found by R. Lyons between capacity and percolation on trees.

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