Abstract
A linear Boltzmann equation is derived in the BoltzmannGrad scaling for the deterministic dynamics of many interacting particles with random initial data. We study a Rayleigh gas where a tagged particle is undergoing hardsphere collisions with background particles, which do not interact among each other. In the BoltzmannGrad scaling, we derive the validity of a linear Boltzmann equation for arbitrary long times under moderate assumptions on higher moments of the initial distributions of the tagged particle and the possibly nonequilibrium distribution of the background. The convergence of the empiric dynamics to the Boltzmann dynamics is shown using Kolmogorov equations for associated probability measures on collision histories.
Original language  English 

Article number  14450 
Pages (fromto)  137177 
Number of pages  41 
Journal  Kinetic and Related Models 
Volume  11 
Issue number  1 
Early online date  16 Aug 2017 
DOIs  
Publication status  Published  1 Feb 2018 
Keywords
 math.AP
 mathph
 math.MP
 Derivation
 Boltzmann equation
 Semigroups
 Rayleigh gas
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Karsten Matthies
 Department of Mathematical Sciences  Senior Lecturer
 Probability Laboratory at Bath
 EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
Person: Research & Teaching