Phase transition in vertex-reinforced random walks on \({\mathbb{Z}}\) with nonlinear reinforcement

DOI10.1007/S10959-006-0033-2zbMath1107.60068OpenAlexW2076251650MaRDI QIDQ867089

Stanislav Volkov

Publication date: 14 February 2007

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10959-006-0033-2

zbMATH Keywords

urn modelsRubin's construction

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Generalized stochastic processes (60G20)

Related Items (9)

VRRW on complete-like graphs: almost sure behavior ⋮ Vertex-reinforced random walk on \(\mathbb Z\) with sub-square-root weights is recurrent ⋮ Localization on 4 sites for vertex-reinforced random walks on \(\mathbb{Z}\) ⋮ Dynamics of vertex-reinforced random walks ⋮ Localization on 5 sites for vertex reinforced random walks: towards a characterization ⋮ Localization of a vertex reinforced random walk on \(\mathbb Z\) with sub-linear weight ⋮ An asymptotic result for Brownian polymers ⋮ Strongly vertex-reinforced jump process on a complete graph ⋮ Vertex-reinforced jump process on the integers with nonlinear reinforcement

Cites Work

• A survey of random processes with reinforcement
• Vertex-reinforced random walk
• A note on vertex-reinforced random walks.
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• Vertex-reinforced random walk on \(\mathbb Z\) has finite range
• Solution to the OK Corral model via decoupling of Friedman's urn
• Vertex-reinforced random walk on arbitrary graphs
• Vertex-reinforced random walk on \(\mathbb Z\) eventually gets stuck on five points.
• Reinforced random walk
• A probabilistic model for the establishment of neuron polarity
• Unnamed Item

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