Linearly edge-reinforced random walks

Abstract

We review results on linearly edge-reinforced random walks. On finite graphs, the process has the same distribution as a mixture of reversible Markov chains. This has applications in Bayesian statistics and it has been used in studying the random walk on infinite graphs. On trees, one has a representation as a random walk in an independent random environment. We review recent results for the random walk on ladders: recurrence, a representation as a random walk in a random environment, and estimates for the position of the random walker.

Published at http://dx.doi.org/10.1214/074921706000000103 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• Bayesian analysis for reversible Markov chains
• Vertex-reinforced random walk on Z eventually gets stuck on five points
• Edge-reinforced random walk on a ladder

Cited by in corpus (8)

• A survey of random processes with reinforcement
• Recurrence of edge-reinforced random walk on a two-dimensional graph
• Anderson localization for a supersymmetric sigma model
• An asymptotic result for Brownian polymers
• Dynamics of vertex-reinforced random walks
• Greedy walk on the real line
• Convergence of vertex-reinforced jump processes to an extension of the supersymmetric hyperbolic nonlinear sigma model
• A functional limit theorem for for excited random walks