Martin capacity for Markov chains

@article{Benjamini1995MartinCF,
  title={Martin capacity for Markov chains},
  author={I. Benjamini and R. Pemantle and Y. Peres},
  journal={Annals of Probability},
  year={1995},
  volume={23},
  pages={1332-1346}
}
The probability that a transient Markov chain, or a Brownian path, will ever visit a given set Λ is classically estimated using the capacity of Λ 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. 

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