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

Anselm Reichenbachs

ESAIM: Probability and Statistics (2013)

  • Volume: 17, page 725-739
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Reichenbachs, Anselm. "Moderate deviations for a Curie–Weiss model with dynamical external field." ESAIM: Probability and Statistics 17 (2013): 725-739. <http://eudml.org/doc/274358>.

@article{Reichenbachs2013,
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.},
author = {Reichenbachs, Anselm},
journal = {ESAIM: Probability and Statistics},
keywords = {moderate deviations; large deviations; statistical mechanics; Curie–Weiss model; dynamic random walks; ergodic theory; Curie-Weiss model},
language = {eng},
pages = {725-739},
publisher = {EDP-Sciences},
title = {Moderate deviations for a Curie–Weiss model with dynamical external field},
url = {http://eudml.org/doc/274358},
volume = {17},
year = {2013},
}

TY - JOUR
AU - Reichenbachs, Anselm
TI - Moderate deviations for a Curie–Weiss model with dynamical external field
JO - ESAIM: Probability and Statistics
PY - 2013
PB - EDP-Sciences
VL - 17
SP - 725
EP - 739
AB - 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.
LA - eng
KW - moderate deviations; large deviations; statistical mechanics; Curie–Weiss model; dynamic random walks; ergodic theory; Curie-Weiss model
UR - http://eudml.org/doc/274358
ER -

References

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