Coupling surfaces and weak Bernoulli in one and higher dimensions
type: Item
instance of: scholarly article
title: Coupling surfaces and weak Bernoulli in one and higher dimensions
zbMATH Open document ID: 0898.60099
author: Jeffrey E. Steif
author: Robert Burton
published in: Advances in Mathematics
publication date: 1998-11-01T00:00:00Z
review text: Since the natural generalization of the definition of weak Bernoulli in dimension 1 to all dimensions is too strong in higher dimensions, the authors propose a different one. It is based on the notion of a coupling surface and, as it is shown, is equivalent to the usual one in dimension 1. The authors study the relation to quite weak Bernoulli and quite weak Bernoulli with exponential rate, introduced by them in [Stochastic Processes Appl. 58, No. 1, 35-55 (1995; Zbl 0835.60088)]. They also show, that the Ising model with large interaction is weak Bernoulli with an explicit construction of the coupling surface.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 28D99
Mathematics Subject Classification ID: 60G60
zbMATH DE Number: 1117790
zbMATH Keywords: weak Bernoulli
zbMATH Keywords: weak Bernoulli with exponential rate
zbMATH Keywords: Ising model
zbMATH Keywords: coupling surface
MaRDI profile type: Publication
full work available at URL: aima.1997.1676
OpenAlex ID: W2027046469
cites work: Q3886625
cites work: A uniqueness condition for Gibbs measures, with application to the 2- dimensional Ising antiferromagnet
cites work: Disagreement percolation in the study of Markov fields
cites work: Percolation and the hard-core lattice gas model
cites work: A caution on mixing conditions for random fields
cites work: Non-uniqueness of measures of maximal entropy for subshifts of finite type
cites work: New results on measures of maximal entropy
cites work: Quite weak Bernoulli with exponential rate and percolation for random fields
cites work: Exponential decay of connectivities in the two-dimensional Ising model
cites work: On isomorphism of weak Bernoulli transformations
cites work: Maximal coupling
cites work: Markov processes, Bernoulli schemes, and Ising model
cites work: A simple coupling of renewal processes
cites work: Approach to equilibrium of Glauber dynamics in the one phase region. I: The attractive case
cites work: Q4049307
cites work: Complete analyticity for 2D Ising completed
cites work: Space-time Bernoullicity of the lower and upper stationary processes for attractive spin systems
cites work: Consistent estimation of joint distributions for sufficiently mixing random fields
cites work: Some Limit Theorems for Random Functions. I
DOI: 10.1006/AIMA.1997.1676
description: scientific article; zbMATH DE number 1117790