A note on the recurrence of edge reinforced random walks
Probability
2009-11-30 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0911.5255,
title = {A note on the recurrence of edge reinforced random walks},
author = {Laurent Tournier},
journal= {arXiv preprint arXiv:0911.5255},
year = {2009}
}
Comments
2 pages