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

Journal Article (2018)
Author(s)

F. Collet (TU Delft - Applied Probability)

RICHARD C. KRAAIJ (Ruhr-Universität Bochum)

Research Group
Applied Probability
Copyright
© 2018 F. Collet, R.C. Kraaij
DOI related publication
https://doi.org/10.1214/17-EJP117
More Info
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Publication Year
2018
Language
English
Copyright
© 2018 F. Collet, R.C. Kraaij
Research Group
Applied Probability
Volume number
23
Pages (from-to)
1-45
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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 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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