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Exit Event from a Metastable State and Eyring-Kramers Law for the Overdamped Langevin Dynamics

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Stochastic Dynamics Out of Equilibrium (IHPStochDyn 2017)

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Abstract

In molecular dynamics, several algorithms have been designed over the past few years to accelerate the sampling of the exit event from a metastable domain, that is to say the time spent and the exit point from the domain. Some of them are based on the fact that the exit event from a metastable region is well approximated by a Markov jump process. In this work, we present recent results on the exit event from a metastable region for the overdamped Langevin dynamics obtained in [22, 23, 56]. These results aim in particular at justifying the use of a Markov jump process parametrized by the Eyring-Kramers law to model the exit event from a metastable region.

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Notes

  1. 1.

    Actually, all the results presented in this section are proved in [22, 23] in the more general setting: \(\overline{\varOmega }=\varOmega \cup \partial \varOmega \) is a \(C^{\infty }\) oriented compact and connected Riemannian manifold of dimension d with boundary \(\partial \varOmega \).

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Acknowledgements

This work is supported by the European Research Council under the European Union’s Seventh Framework Programme (FP/2007–2013)/ERC Grant Agreement number 614492.

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Authors and Affiliations

  1. École des Ponts, Université Paris-Est, Inria, 77455, Champs-sur-Marne, France

    Tony Lelièvre & Boris Nectoux

  2. Laboratoire de Mathématiques d’Orsay, Univ. Paris-Sud, CNRS, Université Paris-Saclay, 91405, Orsay, France

    Dorian Le Peutrec

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  1. Tony Lelièvre
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  2. Dorian Le Peutrec
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  3. Boris Nectoux
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Correspondence to Boris Nectoux .

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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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Lelièvre, T., Le Peutrec, D., Nectoux, B. (2019). Exit Event from a Metastable State and Eyring-Kramers Law for the Overdamped Langevin Dynamics. 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_9

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