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2017 Path large deviations for interacting diffusions with local mean-field interactions in random environment
Patrick E. Müller
Electron. J. Probab. 22: 1-56 (2017). DOI: 10.1214/17-EJP94

Abstract

We consider a system of $N^{d}$ spins in random environment with a random local mean-field type interaction. Each spin has a fixed spatial position on the torus $\mathbb{T} ^{d}$, an attached random environment and a spin value in $\mathbb{R} $ that evolves according to a space and environment dependent Langevin dynamic. The interaction between two spins depends on the spin values, the spatial distance and the random environment of both spins. We prove the path large deviation principle from the hydrodynamic (or local mean-field McKean-Vlasov) limit and derive different expressions of the rate function for the empirical process and for the empirical measure of the paths. To this end we generalize an approach of Dawson and Gärtner.

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Patrick E. Müller. "Path large deviations for interacting diffusions with local mean-field interactions in random environment." Electron. J. Probab. 22 1 - 56, 2017. https://doi.org/10.1214/17-EJP94

Information

Received: 29 January 2017; Accepted: 14 August 2017; Published: 2017
First available in Project Euclid: 16 September 2017

zbMATH: 06797886
MathSciNet: MR3710796
Digital Object Identifier: 10.1214/17-EJP94

Subjects:
Primary: 60F10, 60K35, 82C22

JOURNAL ARTICLE
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