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July 2018 Phase transition for the Once-reinforced random walk on $\mathbb{Z}^{d}$-like trees
Daniel Kious, Vladas Sidoravicius
Ann. Probab. 46(4): 2121-2133 (July 2018). DOI: 10.1214/17-AOP1222

Abstract

In this short paper, we consider the Once-reinforced random walk with reinforcement parameter $a$ on trees with bounded degree which are transient for the simple random walk. On each of these trees, we prove that there exists an explicit critical parameter $a_{0}$ such that the Once-reinforced random walk is almost surely recurrent if $a>a_{0}$ and almost surely transient if $a<a_{0}$. This provides the first examples of phase transition for the Once-reinforced random walk.

Citation

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Daniel Kious. Vladas Sidoravicius. "Phase transition for the Once-reinforced random walk on $\mathbb{Z}^{d}$-like trees." Ann. Probab. 46 (4) 2121 - 2133, July 2018. https://doi.org/10.1214/17-AOP1222

Information

Received: 1 May 2016; Revised: 1 June 2017; Published: July 2018
First available in Project Euclid: 13 June 2018

zbMATH: 06919020
MathSciNet: MR3813987
Digital Object Identifier: 10.1214/17-AOP1222

Subjects:
Primary: 60K35

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.46 • No. 4 • July 2018
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