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Chains with Complete Connections and One-Dimensional Gibbs Measures

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Chains with Complete Connections and One-Dimensional Gibbs Measures
2.	Creator	Author's name, affiliation, country	Roberto Fernandez; Laboratoire de mathematiques Raphael Salem, Universite de Rouen
2.	Creator	Author's name, affiliation, country	Gregory Maillard; Laboratoire de mathematiques Raphael Salem, Universite de Rouen
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Discrete-time processes, Chains with complete connections, Gibbs measures, Markov chains
3.	Subject	Subject classification	60G07; 82B05; 60G10; 60G60; 60J05; 60J10
4.	Description	Abstract	We discuss the relationship between one-dimensional Gibbs measures and discrete-time processes (chains). We consider finite-alphabet (finite-spin) systems, possibly with a grammar (exclusion rule). We establish conditions for a stochastic process to define a Gibbs measure and vice versa. Our conditions generalize well known equivalence results between ergodic Markov chains and fields, as well as the known Gibbsian character of processes with exponential continuity rate. Our arguments are purely probabilistic; they are based on the study of regular systems of conditional probabilities (specifications). Furthermore, we discuss the equivalence of uniqueness criteria for chains and fields and we establish bounds for the continuity rates of the respective systems of finite-volume conditional probabilities. As an auxiliary result we prove a (re)construction theorem for specifications starting from single-site conditioning, which applies in a more general setting (general spin space, specifications not necessarily Gibbsian).
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2004-02-25
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/149
10.	Identifier	Digital Object Identifier	10.1214/EJP.v9-149
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 9
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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