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On large deviations for particle systems associated with spatially homogeneous Boltzmann type equations
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  • Published: March 1995

On large deviations for particle systems associated with spatially homogeneous Boltzmann type equations

  • C. Léonard1 

Probability Theory and Related Fields volume 101, pages 1–44 (1995)Cite this article

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Summary

We consider a dynamical interacting particle system whose empirical distribution tends to the solution of a spatially homogeneous Boltzmann type equation, as the number of particles tends to infinity. These laws of large numbers were proved for the Maxwellian molecules by H. Tanaka [Tal] and for the hard spheres by A.S. Sznitman [Szl]. In the present paper we investigate the corresponding large deviations: the large deviation upper bound is obtained and, using convex analysis, a non-variational formulation of the rate function is given. Our results hold for Maxwellian molecules with a cutoff potential and for hard spheres.

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Authors and Affiliations

  1. Equipe de Modélisation Stochastique et Statistique, U.R.A. CNRS D 0743, Université de Paris-Sud, Départment de Mathématiques, Bâtiment 425, F-91405, Orsay Cedex, France

    C. Léonard

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  1. C. Léonard
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Léonard, C. On large deviations for particle systems associated with spatially homogeneous Boltzmann type equations. Probab. Th. Rel. Fields 101, 1–44 (1995). https://doi.org/10.1007/BF01192194

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  • Received: 11 June 1991

  • Revised: 10 May 1994

  • Issue Date: March 1995

  • DOI: https://doi.org/10.1007/BF01192194

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Mathematics Subject Classification (1991)

  • 60F10
  • 60G57
  • 60K35
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