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Stochastic Mean-Field Dynamics and Applications to Life Sciences

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Stochastic Dynamics Out of Equilibrium (IHPStochDyn 2017)

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Abstract

Although we do not intend to give a general, formal definition, the stochastic mean-field dynamics we present in these notes can be conceived as the random evolution of a system comprised by N interacting components which is: (a) invariant in law for permutation of the components; (b) such that the contribution of each component to the evolution of any other is of order \(\frac{1}{N}\). The permutation invariance clearly does not allow any freedom in the choice of the geometry of the interaction; however, this is exactly the feature that makes these models analytically treatable, and therefore attractive for a wide scientific community.

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Acknowledgement

The author is grateful to an anonymous referee for his careful reading and the useful comments and corrections.

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Authors and Affiliations

  1. Dipartimento di Matematica “Tullio Levi-Civita”, Università di Padova, Padua, Italy

    Paolo Dai Pra

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  1. Paolo Dai Pra
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Correspondence to Paolo Dai Pra .

Editor information

Editors and Affiliations

  1. Laboratoire de Probabilités, Statistiques et Modélisation (UMR 8001), Université Paris Diderot, Paris, France

    Giambattista Giacomin

  2. CEREMADE, CNRS UMR 7534, Université Paris Dauphine - PSL, Paris, France

    Stefano Olla

  3. CNRS UMR 8145, MAP5, Université Paris Descartes, Paris, France

    Ellen Saada

  4. Zentrum Mathematik, Technische Universität München, Garching, Bayern, Germany

    Herbert Spohn

  5. CERMICS, Ecole des Ponts, Marne-La-Vallée, France

    Gabriel Stoltz

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Dai Pra, P. (2019). Stochastic Mean-Field Dynamics and Applications to Life Sciences. In: Giacomin, G., Olla, S., Saada, E., Spohn, H., Stoltz, G. (eds) Stochastic Dynamics Out of Equilibrium. IHPStochDyn 2017. Springer Proceedings in Mathematics & Statistics, vol 282. Springer, Cham. https://doi.org/10.1007/978-3-030-15096-9_1

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