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

Alan D. Sokal, Lawrence E. Thomas

    Research output: Contribution to journalArticle

    Abstract

    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
    Volume54
    Issue number3-4
    DOIs
    StatePublished - Feb 1989

    Fingerprint

    Geometric Ergodicity
    Cayley Tree
    Convergence to Equilibrium
    Exponential Convergence
    Self-avoiding Walk
    Rooted Trees
    Monte Carlo Algorithm
    Autocorrelation
    random walk
    Random walk
    Generalise
    autocorrelation
    apexes
    Model
    Class

    Keywords

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

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Physics and Astronomy(all)
    • Mathematical Physics

    Cite this

    Exponential convergence to equilibrium for a class of random-walk models. / Sokal, Alan D.; Thomas, Lawrence E.

    In: Journal of Statistical Physics, Vol. 54, No. 3-4, 02.1989, p. 797-828.

    Research output: Contribution to journalArticle

    Sokal, Alan D. ; Thomas, Lawrence E. / Exponential convergence to equilibrium for a class of random-walk models. In: Journal of Statistical Physics. 1989 ; Vol. 54, No. 3-4. pp. 797-828.
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