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SUMMARY:Quantitative chaos propagation estimates for jump processes - Clem
 ent Mouhot (CNRS &amp\; Cambridge)
DTSTART:20100209T163000Z
DTEND:20100209T173000Z
UID:TALK23106@talks.cam.ac.uk
CONTACT:Berestycki
DESCRIPTION:This talk devoted to a joint work in collaboration with Stepha
 ne Mischler about the mean-field limit for systems of indistinguables part
 icles undergoing collision processes. As formulated by [Kac\, 1956] this l
 imit is based on the chaos propagation\, and we (1) prove and quantify thi
 s property for Boltzmann collision processes with unbounded collision rate
 s (hard spheres or long-range interactions)\, (2) prove and quantify this 
 property \\emph{uniformly in time}. This yields the first chaos propagatio
 n result for the spatially homogeneous Boltzmann equation for true (withou
 t cut-off) Maxwell molecules whose “Master equation” shares similariti
 es with the one of a Lévy process and the first quantitative chaos propag
 ation result for the spatially homogeneous Boltzmann equation for hard sph
 eres (improvement of the convergence result of [Sznitman\, 1984]). Moreove
 r our chaos propagation results are the first uniform in time ones for Bol
 tzmann collision processes (to our knowledge)\, which partly answers the i
 mportant question raised by Kac of relating the long-time behavior of a pa
 rticle system with the one of its mean-field limit. Our results are based 
 on a new method which reduces the question of chaos propagation to the one
  of proving a purely functional estimate on some generator operators (cons
 istency estimate) together with fine stability estimates on the flow of th
 e limiting non-linear equation (stability estimates). 
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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