Localization on 5 sites for vertex reinforced random walks: Towards a characterization

2019/05/15 by Bruno Schapira, Schapira, Bruno
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1905.05974

14 pages, Revised version. Accepted to Ann. Appl. Probab

arxiv created 2020/10/23 · arxiv updated 2020/10/26

Abstract

We continue the investigation of the localization phenomenon for a Vertex Reinforced Random Walk on the integer lattice. We provide some partial results towards a full characterization of the weights for which localization on 5 sites occurs with positive probability, and make some conjecture concerning the almost sure behavior.

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