Path-space moderate deviation principles for the random field Curie-Weiss model

Francesca Collet; Richard C. Kraaij

doi:10.1214/17-ejp117

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arXiv · 1705.00988

Path-space moderate deviation principles for the random field Curie-Weiss model

Francesca Collet·Richard C. Kraaij

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Abstract

We analyze the dynamics of moderate fluctuations for macroscopic observables of the random field Curie Weiss model (i.e., standard Curie-Weiss model embedded in a site dependent, i.i.d. random environment). We obtain path space large deviation principles via a general analytic approach based on convergence of non-linear generators and uniqueness of viscosity solutions for associated Hamilton Jacobi equations. The moderate asymptotics depend crucially on the phase we consider and moreover, the space-time scale range for which fluctuations can be proven is restricted by the addition of the disorder.

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Francesca Collet, Richard C. Kraaij. 2017-05-02. Path-space moderate deviation principles for the random field Curie-Weiss model. https://doi.org/10.1214/17-ejp117

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