Bounds on the l2spectrum for markov chains and markov processes: A generalization of cheeger’s inequality

Gregory F. Lawler, Alan D. Sokal

    Research output: Contribution to journalArticle

    Abstract

    We prove a general version of Cheeger’s inequality for discretetime Markov chains and continuous-time Markovian jump processes, both reversible and nonreversible, with general state space. We also prove a version of Cheeger’s inequality for Markov chains and processes with killing. As an application, we prove L2exponential convergence to equilibrium for random walk with inward drift on a class of countable rooted graphs.

    Original languageEnglish (US)
    Pages (from-to)557-580
    Number of pages24
    JournalTransactions of the American Mathematical Society
    Volume309
    Issue number2
    DOIs
    StatePublished - 1988

    Fingerprint

    Markov Process
    Markov processes
    Markov chain
    Markovian Process
    Convergence to Equilibrium
    Jump Process
    Countable
    Continuous Time
    Random walk
    State Space
    Discrete-time
    Graph in graph theory
    Generalization
    Class

    ASJC Scopus subject areas

    • Mathematics(all)
    • Applied Mathematics

    Cite this

    Bounds on the l2spectrum for markov chains and markov processes : A generalization of cheeger’s inequality. / Lawler, Gregory F.; Sokal, Alan D.

    In: Transactions of the American Mathematical Society, Vol. 309, No. 2, 1988, p. 557-580.

    Research output: Contribution to journalArticle

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