Moderate Deviations for a Curie-Weiss model with dynamical external field

TL;DR

This paper establishes moderate deviation principles for a Curie-Weiss model influenced by a dynamical external magnetic field, extending previous results and connecting to dynamic Z-random walks.

Contribution

It extends moderate deviation results from constant to dynamical external fields in the Curie-Weiss model and links these results to dynamic Z-random walks.

Findings

Proved moderate deviations for the Curie-Weiss model with dynamical external field.

Extended previous results from constant to dynamical external fields.

Established moderate deviation results for dynamic Z-random walks.

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. The results extend those already obtained in the case of a constant external field by Eichelsbacher and L\"owe. The Curie-Weiss model with dynamic external field is related to the so called dynamic Z-random walks. We also prove a moderate deviation result for the dynamic Z-random walk, completing the list of limit theorems for this object.