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Large Population Asymptotics for Interacting Diffusions in a Quenched Random Environment

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Book cover From Particle Systems to Partial Differential Equations II

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 129))

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Abstract

We review some recent results on large population behavior of interacting diffusions in a random environment. Emphasis is put on the quenched influence of the environment on the macroscopic behavior of the system (law of large numbers and fluctuations). We address the notion of (non-)self-averaging phenomenon for this class of models. A guiding thread in this survey is the Kuramoto synchronization model which has met in recent years a growing interest in the literature.

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Acknowledgments

One of the articles reviewed here [41] was written at the Technische Universität of Berlin and was supported by the BMBF, FKZ 01GQ 1001B.

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  1. Laboratoire MAP 5 (UMR CNRS 8145), Université Paris Descartes, Sorbonne Paris Cité, 45 rue des Saints-Pères, 75270, Paris cedex 06, France

    Eric Luçon

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Correspondence to Eric Luçon .

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  1. Centre of Mathematics, University of Minho, Braga, Portugal

    Patrícia Gonçalves

  2. Centre of Mathematics, University of Minho, Braga, Portugal

    Ana Jacinta Soares

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Luçon, E. (2015). Large Population Asymptotics for Interacting Diffusions in a Quenched Random Environment. In: Gonçalves, P., Soares, A. (eds) From Particle Systems to Partial Differential Equations II. Springer Proceedings in Mathematics & Statistics, vol 129. Springer, Cham. https://doi.org/10.1007/978-3-319-16637-7_8

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