Markov Chain Intersections and the Loop-Erased Walk
Probability
2015-06-26 v2
Abstract
Let X and Y be independent transient Markov chains on the same state space that have the same transition probabilities. Let L denote the ``loop-erased path'' obtained from the path of X by erasing cycles when they are created. We prove that if the paths of X and Y have infinitely many intersections a.s., then L and Y also have infinitely many intersections a.s.
Keywords
Cite
@article{arxiv.math/0107055,
title = {Markov Chain Intersections and the Loop-Erased Walk},
author = {Russell Lyons and Yuval Peres and Oded Schramm},
journal= {arXiv preprint arXiv:math/0107055},
year = {2015}
}
Comments
To appear in Ann. Inst. H. Poincar\'e Probab. Statist