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

Jun Chen; Gady Kozma

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arXiv · 1401.1036

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

Jun Chen·Gady Kozma

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Abstract

We prove that vertex-reinforced random walk on the integers with weight of order k to the power alpha, for alpha in [0, 1/2), is recurrent. This confirms a conjecture of Volkov for alpha<1/2. The conjecture for alpha in [1/2, 1) remains open.

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BibTeX RIS

Jun Chen, Gady Kozma. 2014-01-06. Vertex-reinforced random walk on Z with sub-square-root weights is recurrent. https://arxiv.org/abs/1401.1036

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