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DTSTART:19700329T020000
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DTSTAMP:20221107T160607Z
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DTSTART;TZID=Europe/Berlin:20221110T141500
DTEND;TZID=Europe/Berlin:20221110T151500
SUMMARY:Oberseminar Analysis - Corentin Le Bihan (ENS de Lyon)
DESCRIPTION:Title: Dynamical correlation of the Gibbs measure of a gas in low density scaling\n\nAbstract:\n\nWe consider a gas of N particles in a box of dimension\, interacting pairwise with a potential 𝛼V(r/𝜀). We want to understand the behavior of the system in the limit N->∞\, with a suitable scaling for 𝛼 and 𝜀. If we choose 𝜀=1\, 𝛼=1/N\, it is the mean field limit: particles interact weakly at long distance. We are interested in the low density limit 𝜀=N^{-1/2}\, 𝛼=1. Then the distance crossed by a particle is constant. This limit is well understood since the work of Lanford: the empirical law of the system converges in law to solution of the Boltzmann equation. It is a kind of Law of Large Numbers. Sadly this convergence occurs only for short time. In order to go longer\, we need look at the fluctuations around the equilibrium\, which are supposed to follow a linearized version of Boltzmann equation. The talk will present the idea of the proof of Bodineau\, Gallagher\, Saint Raymond and Simonella for hard sphere potential and the idea of an improvement in case of real interaction potential.
LOCATION:Endenicher Allee 60
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