Journal of Statistical Physics

, Volume 166, Issue 6, pp 1405–1440 | Cite as

Quenched Large Deviations for Interacting Diffusions in Random Media

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Abstract

The aim of the paper is to establish a large deviation principle (LDP) for the empirical measure of mean-field interacting diffusions in a random environment. The point is to derive such a result once the environment has been frozen (quenched model). The main theorem states that a LDP holds for every sequence of environment satisfying appropriate convergence condition, with a rate function that does not depend on the disorder and is different from the rate function in the averaged model. Similar results concerning the empirical flow and local empirical measures are provided.

Keywords

Mean-field particle systems Large deviation principle Disordered systems Sanov theorem 

Mathematics Subject Classification

60F10 60K35 82B44 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Université Paris Descartes, Sorbonne Paris Cité, Laboratoire MAP5, UMR 8145ParisFrance

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