Path-space moderate deviation principles for the random field curie-weiss model

Journal article (2018)

Authors

F. Collet Applied Probability - EEMCS
R.C. Kraaij Ruhr-Universität Bochum
Research Group
Applied Probability (EEMCS) (TU Delft)
Copyright: © 2018 F. Collet, R.C. Kraaij
DOI
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https://doi.org/10.1214/17-EJP117
Mean-field interaction Interacting particle systems Moderate deviations Perturbation theory for Markov processes Hamilton-jacobi equation Quenched random environment
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Published Date

2018

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Applied Probability

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 moderate deviation principles via a general analytic approach based on convergence of nonlinear 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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