Exponential convergence to equilibrium for a class of random-walk models

Alan D. Sokal, Lawrence E. Thomas

    Research output: Contribution to journalArticlepeer-review


    We prove exponential convergence to equilibrium (L2 geometric ergodicity) for a random walk with inward drift on a sub-Cayley rooted tree. This randomwalk model generalizes a Monte Carlo algorithm for the self-avoiding walk proposed by Berretti and Sokal. If the number of vertices of level N in the tree grows as CNNNγ-1, we prove that the autocorrelation time τ satisfies 〈N〉2 ≲ τ ≲ 〈N〉1+γ

    Original languageEnglish (US)
    Pages (from-to)797-828
    Number of pages32
    JournalJournal of Statistical Physics
    Issue number3-4
    StatePublished - Feb 1989


    • Markov chain
    • Monte Carlo
    • dynamic critical phenomena
    • geometric ergodicity
    • random walk
    • self-avoiding walk

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics


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