Geodesic
Moderate deviations for a Curie-Weiss model with dynamical external field
ESAIM: Probability and Statistics, Tome 17 (2013), pp. 725-739

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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.

DOI : 10.1051/ps/2012019
Classification : 60F10, 60K35, 82B44, 82B41, 60G50
Keywords: moderate deviations, large deviations, statistical mechanics, Curie-Weiss model, dynamic random walks, ergodic theory 
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     author = {Reichenbachs, Anselm},
     title = {Moderate deviations for a {Curie-Weiss} model with dynamical external field},
     journal = {ESAIM: Probability and Statistics},
     pages = {725--739},
     publisher = {EDP-Sciences},
     volume = {17},
     year = {2013},
     doi = {10.1051/ps/2012019},
     mrnumber = {3126159},
     zbl = {1290.60105},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2012019/}
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Reichenbachs, Anselm. Moderate deviations for a Curie-Weiss model with dynamical external field. ESAIM: Probability and Statistics, Tome 17 (2013), pp. 725-739. doi: 10.1051/ps/2012019

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