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August 2021 Localization on 5 sites for vertex reinforced random walks: Towards a characterization
Bruno Schapira
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Ann. Appl. Probab. 31(4): 1774-1786 (August 2021). DOI: 10.1214/20-AAP1633

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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Bruno Schapira. "Localization on 5 sites for vertex reinforced random walks: Towards a characterization." Ann. Appl. Probab. 31 (4) 1774 - 1786, August 2021. https://doi.org/10.1214/20-AAP1633

Information

Received: 1 June 2020; Published: August 2021
First available in Project Euclid: 15 September 2021

Digital Object Identifier: 10.1214/20-AAP1633

Subjects:
Primary: 60K35

Keywords: Self-interacting random walks , vertex reinforced random walk

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.31 • No. 4 • August 2021
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