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Scaling limits for the generalized Langevin equation

Grigorios A. Pavliotis 1 Gabriel Stoltz 2, 3 Urbain Vaes 1, 3, 2
3 MATHERIALS - MATHematics for MatERIALS
CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique, Inria de Paris
Abstract : In this paper, we study the diffusive limit of solutions to the generalized Langevin equation (GLE) in a periodic potential. Under the assumption of quasi-Markovianity, we obtain sharp longtime equilibration estimates for the GLE using techniques from the theory of hypocoercivity. We then prove asymptotic results for the effective diffusion coefficient in three limiting regimes: the short memory, the overdamped and the underdamped limits. Finally, we employ a recently developed spectral numerical method in order to calculate the effective diffusion coefficient for a wide range of (effective) friction coefficients, confirming our asymptotic results.
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https://hal.archives-ouvertes.fr/hal-02911852
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Submitted on : Tuesday, August 4, 2020 - 5:56:22 PM
Last modification on : Thursday, February 4, 2021 - 4:50:01 PM

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Grigorios A. Pavliotis, Gabriel Stoltz, Urbain Vaes. Scaling limits for the generalized Langevin equation. Journal of Nonlinear Science, Springer Verlag, 2021, 31, pp.8. ⟨10.1007/s00332-020-09671-4⟩. ⟨hal-02911852⟩

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