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

2011/07/13 by Bruno Schapira, Schapira, Bruno
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1107.2505

Final version, to appear in ECP, 8p

arxiv created 2012/06/14 · arxiv updated 2012/06/15

Abstract

We prove that Vertex Reinforced Random Walk on ℤ with weight of order k^α, with α∈ [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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