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Linearly edge-reinforced random walks

Franz Merkl·Silke W. W. Rolles
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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.

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BibTeXRIS

Franz Merkl, Silke W. W. Rolles. 2006-08-09. Linearly edge-reinforced random walks. https://doi.org/10.1214/074921706000000103

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