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

Abstract

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).

References in corpus (3)

• A survey of random processes with reinforcement
• Vertex-reinforced random walk on Z eventually gets stuck on five points
• Localization of reinforced random walks

Cited by in corpus (1)

• Vertex-reinforced random walk on Z with sub-square-root weights is recurrent