Recurrence of random walks in the Ising spins
type: Item
instance of: scholarly article
title: Recurrence of random walks in the Ising spins
zbMATH Open document ID: 0607.60096
DOI: 10.1007/BF01220512
author: Munemi Miyamoto
published in: Communications in Mathematical Physics
publication date: 1985-01-01T00:00:00Z
review text: Consider the 1/2-Ising model in \(Z^ 2\). Let \(\sigma_ j\) be the spin at the site \((j,0)\in Z^ 2\), \((j=0,\pm 1,\pm 2,...)\). Let \(\{X_ n\}^{+\infty}_{n=0}\) be a random walk with the random transition probabilities such that \[ P(X_{n+1}=j\pm 1| X_ n=j)=p_ j^{\pm}\equiv 1/2\pm \nu (\sigma_ j-\mu)/2. \] We show a case where \(E[p^+_ j]>E[p^-_ j]\), but \(\lim_{n\to \infty}X_ n=-\infty\) a.s. or \(X_ n\) is recurrent a.s.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 82B10
zbMATH DE Number: 3982238
zbMATH Keywords: Ising model
zbMATH Keywords: random walk with the random transition probabilities
zbMATH Keywords: recurrent
MaRDI profile type: Publication
cites work: Q3268576
cites work: Mixing properties in lattice systems
cites work: Q5535438
cites work: Martin-Dynkin boundaries of random fields
cites work: Random walks in a random environment
description: scientific article; zbMATH DE number 3982238