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Stationary measures and phase transition for a class of Probabilistic Cellular Automata

Published online by Cambridge University Press:  15 November 2002

Paolo Dai Pra ,
Pierre-Yves Louis  and
Sylvie Rœlly
Paolo Dai Pra
Affiliation:
Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Belzoni 7, 35131 Padova, Italy; daipra@math.unipd.it.
Pierre-Yves Louis
Affiliation:
Laboratoire de Statistique et Probabilités, FRE 2222 du CNRS, UFR de Mathématiques, Université Lille 1, 59655 Villeneuve-d'Ascq Cedex, France; louis@lps.univ-lille1.fr.
Sylvie Rœlly
Affiliation:
Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstraße 39, 10117 Berlin, Germany; roelly@wias-berlin.de. : CMAP, UMR 7641 du CNRS, École Polytechnique, 91128 Palaiseau Cedex, France.
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Abstract

We discuss various properties of Probabilistic Cellular Automata, suchas the structure of the set of stationary measures and multiplicity ofstationary measures (or phase transition) for reversible models.

Keywords

Probabilistic Cellular Automatastationary measureGibbsmeasure.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 6: New directions in Time Series Analysis (Guest Editor: Philippe Soulier)New directions in Time Series Analysis (Guest Editor: Philippe Soulier) , 2002 , pp. 89 - 104
Copyright
© EDP Sciences, SMAI, 2002

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