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Let X and Y be independent transient Markov chains on the same state spacethat have the same transition probabilities. Let L denote the ``loop-erasedpath'' obtained from the path of X by erasing cycles when they are created. Weprove 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.Comment: To appear in Ann. Inst. H. Poincar\'e Probab. Statis

Markov chain intersections and the loop-erased walk