Phase Transition in Vertex-Reinforced Random Walks on $${\mathbb{Z}}$$ with Non-linear Reinforcement

Stanislav Volkov ()
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Stanislav Volkov: University of Bristol

Journal of Theoretical Probability, 2006, vol. 19, issue 3, 691-700

Abstract: Vertex-reinforced random walk is a random process which visits a site with probability proportional to the weight w k of the number k of previous visits. We show that if w k ∼ k α, then there is a large time T 0 such that after T 0 the walk visits 2, 5, or ∞ sites when α 1, respectively. More general results are also proven.

Keywords: Vertex-reinforced random walks; urn models; Rubin’s construction; 60G20; secondary 60K35 (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/s10959-006-0033-2

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