Moderate deviations for a Curie–Weiss model with dynamical external field∗
Ruhr-Universität Bochum, Fakultät für Mathematik, 44780
Received: 4 July 2011
Revised: 3 July 2012
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.
Mathematics Subject Classification: 60F10 / 60K35 / 82B44 / 82B41 / 60G50
Key words: Moderate deviations / large deviations / statistical mechanics / Curie–Weiss model / dynamic random walks / ergodic theory
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