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| HAL : hal-00681681, version 1 |
| DOI : 10.1063/1.3659685 |
| Fiche détaillée |  Récupérer au format |
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| Journal of Mathematical Physics 52, 11 (2011) nc |
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| Trends to equilibrium for a class of relativistic diffusions |
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| Jürgen Angst 1 |
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| (2011) |
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| A large class C of relativistic diffusions with values in the phase-space of special relativity was introduced by Angst and Franchi [J. Math. Phys. 48(8), 083101 (2007)] in order to answer some open questions concerning the asymptotic behavior of two examples of such processes. In particular, the equilibrium measures of these diffusions were explicitly computed, and their hydrodynamic limit was shown to be Brownian. In this paper, we address the question of the trends to equilibrium of the momentum component of the diffusions of the whole class C. We show the existence of a spectral gap using the Lyapounov method and deduce the exponential decay of the distance to equilibrium in L(2)-norm and in total variation. A similar result was obtained recently by Calogero [e-print arXiv:1009.5086v2] for a particular process of the class C. |
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| 1 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| Processus stochastiques |
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| Domaine | : | Physique/Physique mathématique Mathématiques/Physique mathématique Mathématiques/Equations aux dérivées partielles Mathématiques/Probabilités |
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| Brownian motion – diffusion – Lyapunov methods – special relativity – stochastic processes |
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| hal-00681681, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00681681 | |
| oai:hal.archives-ouvertes.fr:hal-00681681 | |
| Contributeur : Marie-Annick Guillemer | |
| Soumis le : Jeudi 22 Mars 2012, 10:09:31 | |
| Dernière modification le : Mardi 11 Septembre 2012, 11:56:40 | |
