Martin Capacity for Markov Chains
Benjamini, Itai ; Pemantle, Robin ; Peres, Yuval
Ann. Probab., Tome 23 (1995) no. 3, p. 1332-1346 / Harvested from Project Euclid
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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 Lyons between capacity and percolation on trees.
Publié le : 1995-07-14
Classification:  Capacity,  Markov chain,  hitting probability,  Brownian motion,  tree,  percolation,  60J45,  60J10,  60J65,  60J15,  60K35 
@article{1176988187,
     author = {Benjamini, Itai and Pemantle, Robin and Peres, Yuval},
     title = {Martin Capacity for Markov Chains},
     journal = {Ann. Probab.},
     volume = {23},
     number = {3},
     year = {1995},
     pages = { 1332-1346},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176988187}
}

Benjamini, Itai; Pemantle, Robin; Peres, Yuval. Martin Capacity for Markov Chains. Ann. Probab., Tome 23 (1995) no. 3, pp.  1332-1346. http://gdmltest.u-ga.fr/item/1176988187/