Open Access
VOL. 48 | 2006 Linearly edge-reinforced random walks
Franz Merkl, Silke W. W. Rolles

Editor(s) Dee Denteneer, Frank den Hollander, Evgeny Verbitskiy

IMS Lecture Notes Monogr. Ser., 2006: 66-77 (2006) DOI: 10.1214/074921706000000103


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: 1 January 2006
First available in Project Euclid: 28 November 2007

zbMATH: 1125.82014
MathSciNet: MR2306189

Digital Object Identifier: 10.1214/074921706000000103

Primary: 82B41
Secondary: 60K35 , 60K37

Keywords: Bayesian statistics , random environment , recurrence , Reinforced random walk

Rights: Copyright © 2006, Institute of Mathematical Statistics

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