### Abstract

We prove exponential convergence to equilibrium (L^{2} 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^{N}N^{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 | |

State | Published - Feb 1989 |

### Fingerprint

### 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

*Journal of Statistical Physics*,

*54*(3-4), 797-828. https://doi.org/10.1007/BF01019776

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

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 54, no. 3-4, pp. 797-828. https://doi.org/10.1007/BF01019776

}

TY - JOUR

T1 - Exponential convergence to equilibrium for a class of random-walk models

AU - Sokal, Alan D.

AU - Thomas, Lawrence E.

PY - 1989/2

Y1 - 1989/2

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 - dynamic critical phenomena

KW - geometric ergodicity

KW - Markov chain

KW - Monte Carlo

KW - random walk

KW - self-avoiding walk

UR - http://www.scopus.com/inward/record.url?scp=0000294203&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000294203&partnerID=8YFLogxK

U2 - 10.1007/BF01019776

DO - 10.1007/BF01019776

M3 - Article

VL - 54

SP - 797

EP - 828

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 3-4

ER -