Institute of Mathematical Statistics Lecture Notes - Monograph Series

Linearly edge-reinforced random walks

Franz Merkl and Silke W. W. Rolles

Full-text: Open access

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.

Chapter information

Source
Dee Denteneer, Frank den Hollander, Evgeny Verbitskiy, eds., Dynamics & Stochastics: Festschrift in honor of M. S. Keane (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 66-77

Dates
First available in Project Euclid: 28 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.lnms/1196285809

Digital Object Identifier
doi:10.1214/074921706000000103

Mathematical Reviews number (MathSciNet)
MR2306189

Zentralblatt MATH identifier
1125.82014

Subjects
Primary: 82B41: Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41]
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60K37: Processes in random environments

Keywords
reinforced random walk random environment recurrence Bayesian statistics

Rights
Copyright © 2006, Institute of Mathematical Statistics

Citation

Merkl, Franz; Rolles, Silke W. W. Linearly edge-reinforced random walks. Dynamics & Stochastics, 66--77, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000103. https://projecteuclid.org/euclid.lnms/1196285809


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