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2012 A $0$-$1$ law for vertex-reinforced random walks on $\mathbb{Z}$ with weight of order $k^\alpha$, $\alpha\in[0,1/2)$
Bruno Schapira
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Electron. Commun. Probab. 17: 1-8 (2012). DOI: 10.1214/ECP.v17-2084

Abstract

We prove that Vertex Reinforced Random Walk on $\mathbb{Z}$ with weight of order $k^\alpha$, with $\alpha\in [0,1/2)$, is either almost surely recurrent or almost surely transient. This improves a previous result of Volkov who showed that the set of sites which are visited infinitely often was a.s. either empty or infinite.

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Bruno Schapira. "A $0$-$1$ law for vertex-reinforced random walks on $\mathbb{Z}$ with weight of order $k^\alpha$, $\alpha\in[0,1/2)$." Electron. Commun. Probab. 17 1 - 8, 2012. https://doi.org/10.1214/ECP.v17-2084

Information

Accepted: 13 June 2012; Published: 2012
First available in Project Euclid: 7 June 2016

zbMATH: 1244.60033
MathSciNet: MR2943105
Digital Object Identifier: 10.1214/ECP.v17-2084

Subjects:
Primary: 60F20
Secondary: 60K35

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