Markov Chain Intersections and the Loop-Erased Walk

Details Markov Chain Intersections and the Loop-Erased Walk Markov Chain Intersections and the Loop-Erased Walk

2001-07-06

arxiv.org/abs/math/0107055v2

Ann.Inst.H.PoincareProbab.Statist.39:779-791,2003

Mathematics

Probability

To appear in Ann. Inst. H. Poincar\'e Probab. Statist

Scientific paper

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.

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