Linearly edge-reinforced random walks
摘要
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.
引用
@article{arxiv.math/0608220,
title = {Linearly edge-reinforced random walks},
author = {Franz Merkl and Silke W. W. Rolles},
journal= {arXiv preprint arXiv:math/0608220},
year = {2007}
}
备注
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)