Linearly edge-reinforced random walks

Details Linearly edge-reinforced random walks Linearly edge-reinforced random walks

2006-08-09

arxiv.org/abs/math/0608220v1

IMS Lecture Notes--Monograph Series 2006, Vol. 48, 66-77

Mathematics

Probability

Published at http://dx.doi.org/10.1214/074921706000000103 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/

Scientific paper

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.

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