A remark on monotonicity for the Glauber dynamics on finite graphs
type: Item
instance of: scholarly article
title: A remark on monotonicity for the Glauber dynamics on finite graphs
zbMATH Open document ID: 1192.82050
author: Tomoyuki Shirai
published in: Proceedings of the Japan Academy. Series A
publication date: 2010-04-08T00:00:00Z
review text: Properties of the spectral gap in the trasition matrix of the Glauber dynamics are investigated, with a focus on a monotonicity hypothesis. Its general validity is still an open problem. It is known that the gap may be monotone decreasing in each coupling constant of the Hamiltonian, for cycles of any length. The present author departs from correlation inequalities (GKS and GHZ) for spin systems to verify whether the single spin expectation for a fixed time in the relaxation process starting from all-up configuration is monotone increasing in each coupling constant. If that would hold true the monotonicity of the spectral gap would follow. The answer is negative (counter example).
reviewed by: Piotr Garbaczewski
Mathematics Subject Classification ID: 82C20
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 5690872
zbMATH Keywords: Ising model
zbMATH Keywords: Glauber dynamics
zbMATH Keywords: spectral gap
zbMATH Keywords: monotonicity conjecture
zbMATH Keywords: correlation inequalities
zbMATH Keywords: spin expectation
MaRDI profile type: Publication
full work available at URL: pjaa.86.33
OpenAlex ID: W2010535053
cites work: Correlation inequalities on some partially ordered sets
cites work: Q3549475
cites work: Glauber dynamics on the cycle is monotone
DOI: 10.3792/PJAA.86.33
description: scientific article; zbMATH DE number 5690872