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.
Mots clés : moderate deviations, large deviations, statistical mechanics, Curie-Weiss model, dynamic random walks, ergodic theory
@article{PS_2013__17__725_0,
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://archive.numdam.org/articles/10.1051/ps/2012019/}
}
TY - JOUR AU - Reichenbachs, Anselm TI - Moderate deviations for a Curie-Weiss model with dynamical external field JO - ESAIM: Probability and Statistics PY - 2013 SP - 725 EP - 739 VL - 17 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2012019/ DO - 10.1051/ps/2012019 LA - en ID - PS_2013__17__725_0 ER -
%0 Journal Article %A Reichenbachs, Anselm %T Moderate deviations for a Curie-Weiss model with dynamical external field %J ESAIM: Probability and Statistics %D 2013 %P 725-739 %V 17 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2012019/ %R 10.1051/ps/2012019 %G en %F PS_2013__17__725_0
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. http://archive.numdam.org/articles/10.1051/ps/2012019/
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