Weighted $L^2$-contractivity of Langevin dynamics with singular potentials
| Autor: | Evan Camrud, David P Herzog, Gabriel Stoltz, Maria Gordina |
|---|---|
| Přispěvatelé: | Department of Mathematics [IOWA], Iowa State University (ISU), Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC), MATHematics for MatERIALS (MATHERIALS), École des Ponts ParisTech (ENPC)-École des Ponts ParisTech (ENPC)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Department of Mathematics [Storrs], University of Connecticut (UCONN), ANR-19-CE40-0010,QuAMProcs,Analyse Quantitative de Processus Metastables(2019), European Project: 810367,EMC2(2019), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC)-École des Ponts ParisTech (ENPC) |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Applied Mathematics
010102 general mathematics Probability (math.PR) General Physics and Astronomy FOS: Physical sciences 60H10 35Q84 60J60 (Primary) 35B40 (Secondary) Statistical and Nonlinear Physics Mathematical Physics (math-ph) 01 natural sciences 010104 statistics & probability Mathematics - Analysis of PDEs FOS: Mathematics 0101 mathematics [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] Mathematics - Probability Mathematical Physics Analysis of PDEs (math.AP) |
| Zdroj: | Nonlinearity Nonlinearity, IOP Publishing, 2022, 35 (2), pp.998-1035 Nonlinearity, 2022, 35 (2), pp.998-1035 |
| ISSN: | 0951-7715 1361-6544 |
| Popis: | Convergence to equilibrium of underdamped Langevin dynamics is studied under general assumptions on the potential U allowing for singularities. By modifying the direct approach to convergence in L 2 pioneered by Hérau and developed by Dolbeault et al, we show that the dynamics converges exponentially fast to equilibrium in the topologies L 2(dμ) and L 2(W* dμ), where μ denotes the invariant probability measure and W* is a suitable Lyapunov weight. In both norms, we make precise how the exponential convergence rate depends on the friction parameter γ in Langevin dynamics, by providing a lower bound scaling as min(γ, γ −1). The results hold for usual polynomial-type potentials as well as potentials with singularities such as those arising from pairwise Lennard-Jones interactions between particles. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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