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Moderate deviations for a Curie–Weiss model with dynamical external field∗

Published online by Cambridge University Press:  04 November 2013

Anselm Reichenbachs
Anselm Reichenbachs*
Affiliation:
Ruhr-Universität Bochum, Fakultät für Mathematik, 44780 Bochum, Germany. anselm.reichenbachs@rub.de
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Abstract

In the present paper we prove moderate deviations for a Curie–Weiss model with external magnetic field generated by a dynamical system, as introduced by Dombry and Guillotin-Plantard in [C. Dombry and N. Guillotin-Plantard, Markov Process. Related Fields 15 (2009) 1–30]. The results extend those already obtained for the Curie–Weiss model without external field by Eichelsbacher and Löwe in [P. Eichelsbacher and M. Löwe, Markov Process. Related Fields 10 (2004) 345–366]. The Curie–Weiss model with dynamical external field is related to the so called dynamic ℤ-random walks (see [N. Guillotin-Plantard and R. Schott, Theory and applications, Elsevier B. V., Amsterdam (2006).]). We also prove a moderate deviation result for the dynamic ℤ-random walk, completing the list of limit theorems for this object.

Keywords

Moderate deviationslarge deviationsstatistical mechanicsCurie–Weiss modeldynamic random walksergodic theory

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Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 17 , 2013 , pp. 725 - 739
Copyright
© EDP Sciences, SMAI, 2013

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