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| HAL: hal-00681681, version 1 |
| DOI: 10.1063/1.3659685 |
| Detailed view |  Export this paper |
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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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| Subject | : | Physics/Mathematical Physics Mathematics/Mathematical Physics Mathematics/Analysis of PDEs Mathematics/Probability |
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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 | |
| From: Marie-Annick Guillemer | |
| Submitted on: Thursday, 22 March 2012 10:09:31 | |
| Updated on: Tuesday, 11 September 2012 11:56:40 | |
