Recurrence for vertex-reinforced random walks on Z with weak reinforcements

2014/01/06 by Arvind Singh, Singh, Arvind · 1 citation
Computer Science · Mathematics · #60K35 #Complexity and Algorithms in Graphs #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR #msc:60K35

paper · pdf · doi:10.48550/arxiv.1401.1034

arxiv created 2014/01/06 · openalex publication_date 2014/01/06 · arxiv updated 2014/01/07 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We prove that any vertex-reinforced random walk on the integer lattice with non-decreasing reinforcement sequence w satisfying w(k) = o(k^α) for some α< 1/2 is recurrent. This improves on previous results of Volkov (2006) and Schapira (2012).

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