Vertex-reinforced random walk on \(\mathbb Z\) with sub-square-root weights is recurrent

DOI10.1016/j.crma.2014.03.019zbMath1307.60049arXiv1401.1036OpenAlexW2962684448MaRDI QIDQ460722

Gady Kozma, Jun Chen

Publication date: 14 October 2014

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.1036

zbMATH Keywords

recurrencyvertex-reinforced random walk

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Zero-one laws (60F20) Continuous-time Markov processes on discrete state spaces (60J27) Applications of continuous-time Markov processes on discrete state spaces (60J28)

Related Items (2)

Two repelling random walks on \(\mathbb{Z}\) ⋮ Localization on 5 sites for vertex reinforced random walks: towards a characterization

Cites Work

• A 0-1 law for vertex-reinforced random walks on \(\mathbb{Z}\) with weight of order \(k^\alpha,\;\alpha\in[0,1/2)\)
• Recurrence for vertex-reinforced random walks on \(\mathbb Z\) with weak reinforcements.
• Phase transition in vertex-reinforced random walks on \({\mathbb{Z}}\) with nonlinear reinforcement
• Vertex-reinforced random walk
• Vertex-reinforced random walk on \(\mathbb Z\) has finite range
• Vertex-reinforced random walk on \(\mathbb Z\) eventually gets stuck on five points.
• Reinforced random walk

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