Colloque des sciences mathématiques du Québec

20 mai 2022 de 15 h 30 à 16 h 30 (heure de Montréal/HNE)

Mathematical analysis of dilute gases : derivation of the Boltzmann equation, fluctuations and large deviations

Colloque par Isabelle Gallagher (Ecole Normale Supérieure)

Titulaire de la Chaire Aisenstadt 2022 

The evolution of a gas can be described by different models depending on the observation scale. A natural question, raised by Hilbert in his sixth problem, is whether these models provide consistent predictions. In particular, for rarefied gases, it is expected that continuum laws of kinetic theory can be obtained directly from molecular dynamics governed by the fundamental principles of mechanics. In the case of hard sphere gases, Lanford showed  in 1975 that the Boltzmann equation emerges as the law of large numbers in the low density limit, at least for very short times. The goal of this talk is to explain the heuristics of his proof and present recent progress in the understanding of this limiting process.