A note on the recurrence of edge reinforced random walks

Details A note on the recurrence of edge reinforced random walks A note on the recurrence of edge reinforced random walks

2009-11-27

arxiv.org/abs/0911.5255v1

Mathematics

Probability

2 pages

Scientific paper

We give a short proof of Theorem 2.1 from [MR07], stating that the linearly edge reinforced random walk (ERRW) on a locally finite graph is recurrent if and only if it returns to its starting point almost surely. This result was proved in [MR07] by means of the much stronger property that the law of the ERRW is a mixture of Markov chains. Our proof only uses this latter property on finite graphs, in which case it is a consequence of De Finetti's theorem on exchangeability.

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