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Markov Chain Intersections and the Loop-Erased Walk

Russell Lyons·Yuval Peres·Oded Schramm
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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.

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Russell Lyons, Yuval Peres, Oded Schramm. 2001-07-06. Markov Chain Intersections and the Loop-Erased Walk. https://doi.org/10.1016/s0246-0203(03)00033-5

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