Attracting edge and strongly edge reinforced walks

DOI10.1214/009117906000001097zbMath1131.60036arXivmath/0604200OpenAlexW1987359907MaRDI QIDQ2456028

Pierre Tarrès, Vlada Limic

Publication date: 17 October 2007

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

Full work available at URL: https://arxiv.org/abs/math/0604200

zbMATH Keywords

martingale techniqueattracting edgereinforced walk

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10)

Related Items (9)

Senile reinforced random walks ⋮ Dynamics of vertex-reinforced random walks ⋮ Vertex reinforced non-backtracking random walks: an example of path formation ⋮ Attraction time for strongly reinforced walks ⋮ An asymptotic result for Brownian polymers ⋮ Linear de-preferential urn models ⋮ Recurrence of edge-reinforced random walk on a two-dimensional graph ⋮ Vertex-reinforced jump process on the integers with nonlinear reinforcement ⋮ The directed edge reinforced random walk: the Ant Mill phenomenon

Cites Work

• Nonconvergence to unstable points in urn models and stochastic approximations
• Attracting edge property for a class of reinforced random walks
• Vertex-reinforced random walk on \(\mathbb Z\) eventually gets stuck on five points.
• Edge-reinforced random walk on a ladder
• On the recurrence of edge-reinforced random walk on \(\mathbb Z \times G\)
• Pièges répulsifs
• Reinforced random walk
• Unnamed Item

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