4.2 Article

T HE BOLTZMANN-GRAD LIMIT FOR THE LORENTZ GAS WITH A POISSON DISTRIBUTION OF OBSTACLES

Journal

KINETIC AND RELATED MODELS
Volume 15, Issue 3, Pages 517-534

Publisher

AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/krm.2022001

Keywords

Key words and phrases; Kinetic theory; Boltzmann equation; Boltzmann-Grad limit; Lorentz gas; Poisson point process

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This note proposes a slightly different proof of Gallavotti's theorem in deriving the linear Boltzmann equation for the Lorentz gas with obstacles following a Poisson distribution in the Boltzmann-Grad limit.
In this note, we propose a slightly different proof of Gallavotti's theorem [Statistical Mechanics: A Short Treatise, Springer, 1999, pp. 48-55] on the derivation of the linear Boltzmann equation for the Lorentz gas with a Poisson distribution of obstacles in the Boltzmann-Grad limit.

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