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| HAL : hal-00392397, version 1 |
| arXiv : 0906.1417 |
| Fiche détaillée |  Récupérer au format |
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| Trend to equilibrium and particle approximation for a weakly selfconsistent Vlasov-Fokker-Planck equation |
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| Francois Bolley 1Arnaud Guillin 2 |
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| (07/06/2009) |
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| We consider a Vlasov-Fokker-Planck equation governing the evolution of the density of interacting and diffusive matter in the space of positions and velocities. We use a probabilistic interpretation to obtain convergence towards equilibrium in Wasserstein distance with an explicit exponential rate. We also prove a propagation of chaos property for an associated particle system, and give rates on the approximation of the solution by the particle system. Finally, a transportation inequality for the distribution of the particle system leads to quantitative deviation bounds on the approximation of the equilibrium solution of the equation by an empirical mean of the particles at given time. |
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| 1 : | CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) |
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CNRS : UMR7534 – Université Paris Dauphine - Paris IX |
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| 2 : | Laboratoire de mathématiques |
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CNRS : UMR6620 – Université Blaise Pascal - Clermont-Ferrand II |
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| 3 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes I – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées de Rennes |
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| Domaine | : | Mathématiques/Probabilités Mathématiques/Equations aux dérivées partielles |
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| Vlasov-Fokker-Planck equation – particle approximation – chaos propagation – transportation inequality |
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| hal-00392397, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00392397/fr/ | |
| oai:hal.archives-ouvertes.fr:hal-00392397_v1 | |
| Contributeur : Arnaud Guillin | |
| Soumis le : Dimanche 7 Juin 2009, 21:56:57 | |
| Dernière modification le : Lundi 8 Juin 2009, 08:33:34 | |
