Localization on 5 sites for vertex reinforced random walks: towards a characterization

DOI10.1214/20-AAP1633zbMath1479.60202arXiv1905.05974OpenAlexW3199833801MaRDI QIDQ2240868

Bruno Schapira

Publication date: 4 November 2021

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.05974

zbMATH Keywords

self-interacting random walksvertex reinforced random walk

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Interacting random processes; statistical mechanics type models; percolation theory (60K35)

Related Items (1)

Lyapunov function for interacting reinforced stochastic processes via Hopfield's energy function

Cites Work

• A 0-1 law for vertex-reinforced random walks on \(\mathbb{Z}\) with weight of order \(k^\alpha,\;\alpha\in[0,1/2)\)
• Vertex-reinforced random walk on \(\mathbb Z\) with sub-square-root weights is recurrent
• Dynamics of vertex-reinforced random walks
• 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.
• Localization of a vertex reinforced random walk on \(\mathbb Z\) with sub-linear weight
• Localization on 4 sites for vertex-reinforced random walks on \(\mathbb{Z}\)
• Probability
• Reinforced random walk

This page was built for publication: Localization on 5 sites for vertex reinforced random walks: towards a characterization