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).
Citation
Arvind Singh. "Recurrence for vertex-reinforced random walks on $\mathbb{Z}$ with weak reinforcements.." Electron. Commun. Probab. 19 1 - 6, 2014. https://doi.org/10.1214/ECP.v19-3242
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