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CATEGORIES:Probability
SUMMARY:Quantitative chaos propagation estimates for jump
processes - Clement Mouhot (CNRS &\; Cambridge)
DTSTART;TZID=Europe/London:20100209T163000
DTEND;TZID=Europe/London:20100209T173000
UID:TALK23106AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/23106
DESCRIPTION:This talk devoted to a joint work in collaboration
with Stephane Mischler about the mean-field limit
for systems of indistinguables particles undergoi
ng collision processes. As formulated by [Kac\, 19
56] this limit is based on the chaos propagation\,
and we (1) prove and quantify this property for B
oltzmann collision processes with unbounded collis
ion rates (hard spheres or long-range interactions
)\, (2) prove and quantify this property \\emph{un
iformly in time}. This yields the first chaos prop
agation result for the spatially homogeneous Boltz
mann equation for true (without cut-off) Maxwell m
olecules whose “Master equation” shares similariti
es with the one of a Lévy process and the first qu
antitative chaos propagation result for the spatia
lly homogeneous Boltzmann equation for hard sphere
s (improvement of the convergence result of [Sznit
man\, 1984]). Moreover our chaos propagation resul
ts are the first uniform in time ones for Boltzman
n collision processes (to our knowledge)\, which p
artly answers the important question raised by Kac
of relating the long-time behavior of a particle
system with the one of its mean-field limit. Our r
esults are based on a new method which reduces the
question of chaos propagation to the one of provi
ng a purely functional estimate on some generator
operators (consistency estimate) together with fin
e stability estimates on the flow of the limiting
non-linear equation (stability estimates).
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Berestycki
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