The Annals of Applied Probability

Nonreversible stationary measures for exchange processes

Amine Asselah

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Abstract

We consider nonreversible exchange dynamics in $Z^d$ and prove that the stationary, translation invariant measures satisfy the following property: if one of them is a Gibbs measure with a summable potential ${J_R, R \subset Z^d}$, then all of them are convex combinations of Gibbs measures with the same potential, but different chemical potentials $J_{\{0\}}$.

Article information

Source
Ann. Appl. Probab., Volume 8, Number 4 (1998), 1303-1311.

Dates
First available in Project Euclid: 9 August 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1028903382

Digital Object Identifier
doi:10.1214/aoap/1028903382

Mathematical Reviews number (MathSciNet)
MR1661196

Zentralblatt MATH identifier
0951.60096

Subjects
Primary: 28D10: One-parameter continuous families of measure-preserving transformations 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82C22: Interacting particle systems [See also 60K35]

Keywords
Relative entropy Gibbs measures nonreversible stationary measures

Citation

Asselah, Amine. Nonreversible stationary measures for exchange processes. Ann. Appl. Probab. 8 (1998), no. 4, 1303--1311. doi:10.1214/aoap/1028903382. https://projecteuclid.org/euclid.aoap/1028903382


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