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

Alan D. Sokal; Lawrence E. Thomas

doi:10.1007/BF01019776

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

Alan D. Sokal, Lawrence E. Thomas

Research output: Contribution to journal › Article › peer-review

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 C_N~μ^NN^γ-1, we prove that the autocorrelation time τ satisfies 〈N〉² ≲ τ ≲ 〈N〉^1+γ

Original language	English (US)
Pages (from-to)	797-828
Number of pages	32
Journal	Journal of Statistical Physics
Volume	54
Issue number	3-4
DOIs	https://doi.org/10.1007/BF01019776
State	Published - Feb 1989

Keywords

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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10.1007/BF01019776

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keywords = "Markov chain, Monte Carlo, dynamic critical phenomena, geometric ergodicity, random walk, self-avoiding walk",

author = "Sokal, {Alan D.} and Thomas, {Lawrence E.}",

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AU - Thomas, Lawrence E.

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N2 - 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 CN~μNNγ-1, we prove that the autocorrelation time τ satisfies 〈N〉2 ≲ τ ≲ 〈N〉1+γ

AB - 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 CN~μNNγ-1, we prove that the autocorrelation time τ satisfies 〈N〉2 ≲ τ ≲ 〈N〉1+γ

KW - Markov chain

KW - Monte Carlo

KW - dynamic critical phenomena

KW - geometric ergodicity

KW - random walk

KW - self-avoiding walk

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JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 3-4

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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