The Annals of Probability

Regenerative Representation for One-Dimensional Gibbs States

S. P. Lalley

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Abstract

It is shown that one-dimensional Gibbs states may be represented as concatenations of infinite lists of iid "words." It follows that Gibbs states inherit many properties of recurrent Markov chains on denumerable state spaces.

Article information

Source
Ann. Probab., Volume 14, Number 4 (1986), 1262-1271.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176992367

Digital Object Identifier
doi:10.1214/aop/1176992367

Mathematical Reviews number (MathSciNet)
MR866347

Zentralblatt MATH identifier
0612.60093

JSTOR
links.jstor.org

Subjects
Primary: 60G10: Stationary processes
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Gibbs state chain with complete connections regenerative representation

Citation

Lalley, S. P. Regenerative Representation for One-Dimensional Gibbs States. Ann. Probab. 14 (1986), no. 4, 1262--1271. doi:10.1214/aop/1176992367. https://projecteuclid.org/euclid.aop/1176992367


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