Martin Capacity for Markov Chains

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dc.creatorBenjamini, Itai
dc.creatorPemantle, Robin
dc.creatorPeres, Yuval
dc.date2004-04-02
dc.date.accessioned2026-07-07T05:07:03Z
dc.date.available2026-07-07T05:07:03Z
dc.descriptionThe 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.
dc.description21 pages
dc.identifierhttps://arxiv.org/abs/math/0404054
dc.identifierhttp://arxiv.org/abs/math/0404054
dc.identifierAnn. Probab., 23, 1332 - 1346 (1995)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70710
dc.subjectProbability
dc.subject60J45, 60J10 (Primary) 60J65, 60J15, 60K35 (Secondary)
dc.titleMartin Capacity for Markov Chains
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