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| HAL : hal-00127988, version 2 |
| arXiv : math/0701879 |
| DOI : 10.1214/07-AAP513 |
| Fiche détaillée |  Récupérer au format |
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| The Annals of Applied Probability 18, 5 (2008) 1706-1736 |
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| Versions disponibles : | v1 (30-01-2007) | v2 (14-11-2008) |
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| Propagation of chaos and Poincaré inequalities for a system of particles interacting through their cdf |
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| Benjamin Jourdain 1Florent Malrieu 2 |
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| (10/2008) |
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| In the particular case of a concave flux function, we are interested in the long time behaviour of the nonlinear process associated to the one-dimensional viscous scalar conservation law. We also consider the particle system obtained by remplacing the cumulative distribution function in the drift coefficient of this nonlinear process by the empirical cdf. We first obtain trajectorial propagation of chaos result. Then, Poincaré inequalities are used to get explicit estimates concerning the long time behaviour of both the nonlinear process and the particle system. |
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| 1 : | Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique (CERMICS) |
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INRIA – Ecole des Ponts ParisTech |
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| 2 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – INSA Rennes – Université Rennes II |
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| CERMICS ; Processus stochastiques |
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| Domaine | : | Mathématiques/Probabilités |
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| viscous scalar conservation law – nonlinear process – interacting particle system – propagation of chaos – Poincaré inequality – long time behavior |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00127988, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00127988 | |
| oai:hal.archives-ouvertes.fr:hal-00127988 | |
| Contributeur : Florent Malrieu | |
| Soumis le : Vendredi 14 Novembre 2008, 14:54:33 | |
| Dernière modification le : Jeudi 18 Mars 2010, 15:10:15 | |
