Electronic Journal of Probability

Path large deviations for interacting diffusions with local mean-field interactions in random environment

Patrick E. Müller

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.

Article information

Source
Electron. J. Probab., Volume 22 (2017), paper no. 76, 56 pp.

Dates
Accepted: 14 August 2017
First available in Project Euclid: 16 September 2017

https://projecteuclid.org/euclid.ejp/1505527232

Digital Object Identifier
doi:10.1214/17-EJP94

Mathematical Reviews number (MathSciNet)
MR3710796

Zentralblatt MATH identifier
06797886

Citation

Müller, Patrick E. Path large deviations for interacting diffusions with local mean-field interactions in random environment. Electron. J. Probab. 22 (2017), paper no. 76, 56 pp. doi:10.1214/17-EJP94. https://projecteuclid.org/euclid.ejp/1505527232

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