Mixing time for the solid-on-solid model
type: Item
instance of: scholarly article
title: Mixing time for the solid-on-solid model
zbMATH Open document ID: 1283.60122
DOI: 10.1214/11-AAP791
author: Fabio Martinelli
author: Alistair Sinclair
published in: The Annals of Applied Probability
publication date: 2012-07-08T00:00:00Z
full work available at URL: https://arxiv.org/abs/1008.0125
full work available at URL: https://projecteuclid.org/euclid.aoap/1337347541
review text: The authors give an upper bound of the mixing time of the Glauber process for the solid-on-solid model, which turns out to be of \(\tilde{O}( n^{\frac{7}{2}})\) and tight within a factor of \(\tilde{O}(\sqrt{n})\). The proof, which in addition gives some insight into the actual evolution of the contours, rests on a careful application of the so-called censoring inequality to bound the mixing time of the local dynamics by that of a non-local one times the mixing time of the one-dimensional local process under which the single site configuration evolves.
reviewed by: Michele Gianfelice
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82C20
zbMATH DE Number: 6053741
zbMATH Keywords: solid-on-solid model
zbMATH Keywords: Markov chain Monte Carlo
zbMATH Keywords: censoring
zbMATH Keywords: Glauber dynamics
zbMATH Keywords: mixing time
zbMATH Keywords: monotonicity
zbMATH Keywords: Ising model
MaRDI profile type: Publication
arXiv ID: 1008.0125
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description: scientific article; zbMATH DE number 6053741