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SUMMARY:Semigroup methods for the derivation of Boltzmann-type equations f
 rom deterministic particle dynamics - Karsten Matthies (University of Bath
 )
DTSTART:20220215T133000Z
DTEND:20220215T141500Z
UID:TALK170132@talks.cam.ac.uk
DESCRIPTION:In this talk we will revisit the classical questions of unders
 tanding the statistics of various deterministic dynamics of n hard spheres
  of diameter a with random initial data in the Boltzmann-Grad scaling as a
  tends to zero and n tends to infinity. I will present some ideas to repla
 ce the analysis of the BBGKY hierarchy. The convergence of the empiric dyn
 amics to the Boltzmann-type dynamics is shown using semigroup methods to a
 nalyse Kolmogorov equations for associated probability measures on genuine
  collision histories.&nbsp\;&nbsp\;\nDetails are given for a Rayleigh gas 
 where a tagged particle is undergoing collisions with background particles
 \, which do not interact among each other. In the Boltzmann-Grad scaling\,
  we derive the validity of a linear Boltzmann equation for arbitrary long 
 times under moderate assumptions on the initial distributions of the tagge
 d particle and the possibly non-equilibrium distribution of the background
 . I aim to give various current and future questions. Based on work with G
 eorge Stone\, Theodora Syntaka and Florian Theil.
LOCATION:Seminar Room 2\, Newton Institute
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