Once reinforced random walk on Z × Γ

Daniel Kious, Bruno Schapira, Arvind Singh

OAI: oai:purehost.bath.ac.uk:openaire_cris_publications/2c1d3730-b9e8-460e-af62-b1ab6ea32772 • DOI: https://doi.org/10.1214/21-AIHP1151

We revisit Vervoort’s unpublished paper (Vervoort (2002)) on the once reinforced random walk, and prove that this process is recurrent on any graph of the form Z × Γ, with Γ a finite graph, for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.

Recurrence reinforced random walk Self-interacting random walk Shape theorem /dk/atira/pure/subjectarea/asjc/2600/2613 name=Statistics and Probability /dk/atira/pure/subjectarea/asjc/1800/1804 name=Statistics, Probability and Uncertainty