A random environment for linearly edge-reinforced walks on infinite graphs

F. Merkl, S.W.W. Rolles

    Research output: Contribution to journalArticleAcademicpeer-review

    12 Citations (Scopus)

    Abstract

    We consider linearly edge-reinforced random walk on an arbitrary locally finite connected graph. It is shown that the process has the same distribution as a mixture of reversible Markov chains, determined by time-independent strictly positive weights on the edges. Furthermore, we prove bounds for the random weights, uniform, among others, in the size of the graph.
    Original languageEnglish
    Pages (from-to)157-176
    JournalProbability Theory and Related Fields
    Volume138
    Issue number1-2
    DOIs
    Publication statusPublished - 2007

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