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arXiv · 1107.2505

A 0-1 law for vertex-reinforced random walks on $\mathbb{Z}$ with weight of order $k^α$, $α<1/2$

Bruno Schapira
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Abstract

We prove that Vertex Reinforced Random Walk on $\mathbb{Z}$ with weight of order $k^α$, with $α\in [0,1/2)$, 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. 2012-06-14. A 0-1 law for vertex-reinforced random walks on $\mathbb{Z}$ with weight of order $k^α$, $α<1/2$. https://arxiv.org/abs/1107.2505

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