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

Arvind Singh

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

Probability 2014-01-07 v1

Authors: Arvind Singh

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).

Keywords

vertex-reinforced random walk recurrence integer lattice weak reinforcement asymptotic behavior

Cite

@article{arxiv.1401.1034,
  title  = {Recurrence for vertex-reinforced random walks on Z with weak reinforcements},
  author = {Arvind Singh},
  journal= {arXiv preprint arXiv:1401.1034},
  year   = {2014}
}

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