On the Boltzmann equation for the Lorentz gas
type: Item
instance of: scholarly article
title: On the Boltzmann equation for the Lorentz gas
zbMATH Open document ID: 0583.76092
DOI: 10.1007/BF01008951
published in: Journal of Statistical Physics
publication date: 1983-01-01T00:00:00Z
review text: We consider the Boltzmann-Grad limit for the Lorentz, or wind-tree, model. We prove that if \(\omega\) is a fixed configuration of scatterer centers belonging to a set of full measure with respect to the Poisson distribution with parameter \(\lambda >0\), then the evolution of an initial a.c. particle density tends in the Boltzmann-Grad limit to the solution of the Boltzmann equation for the model. As an intermediate step we prove that the process of the free path lengths and impact parameters induced by the Lebesgue measure on a small region tends to a limiting independent process.
Mathematics Subject Classification ID: 76P05
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 82B40
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 76N15
zbMATH DE Number: 3934657
zbMATH Keywords: classical Lorentz gas
zbMATH Keywords: wind-tree model
zbMATH Keywords: theory of billiards
zbMATH Keywords: linear Fokker-Planck-Kolmogorov equation
zbMATH Keywords: Boltzmann-Grad limit
zbMATH Keywords: configuration of scatterer centers
zbMATH Keywords: Poisson distribution
zbMATH Keywords: particle density
zbMATH Keywords: free path lengths
zbMATH Keywords: impact parameters
zbMATH Keywords: limiting independent process
author: C. Boldrighini
author: Leonid A. Bunimovich
author: Ya. G. Sinai
MaRDI profile type: Publication
cites work: Dynamical systems with elastic reflections
cites work: Q4087473
cites work: Markov partitions for dispersed billiards
description: scientific article; zbMATH DE number 3934657