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Once reinforced random walk on Z × Γ

Bruno Schapira
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Arvind Singh
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Abstract

We revisit Vervoort's unpublished paper [16] on the once reinforced random walk, and prove that this process is recurrent on any graph of the form Z × Γ, with Γ a finite graph, for sufficiently large reinforcement parameter. We also obtain a shape theorem for the set of visited sites, and show that the fluctuations around this shape are of polynomial order. The proof involves sharp general estimates on the time spent on subgraphs of the ambiant graph which might be of independent interest.
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Dates and versions

hal-01876969 , version 1 (19-09-2018)

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  • HAL Id : hal-01876969 , version 1

Cite

Daniel Kious, Bruno Schapira, Arvind Singh. Once reinforced random walk on Z × Γ. 2018. ⟨hal-01876969⟩
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