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

Arvind Singh (CNRS - Université Paris-Sud)


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

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Pages: 1-6

Publication Date: March 3, 2014

DOI: 10.1214/ECP.v19-3242


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