EVENT DETAILS AND ABSTRACT

Title: Recent progress in Mark Kac's probabilistic program in kinetic theory
Speaker: Eric Carlen
Speaker Info: Rutgers University
Brief Description:
Special Note:
Abstract:

Kinetic theory describes the evolution of dilute gas of particles interacting through binary collisions. The equations of kinetic theory are non-linear evolution equations (various forms of the Boltzmann equation for a probability density. In 1956, Mark Kac proposed a strategy for investigating such equations via a direct analysis of a stochastic model, different from, and simpler than, the underlying physical collision model, but still leading to the same equations. There has been much recent progress on Kac's program. We shall discuss recent work on determining the rate of equilibriation in this model. Until now, this had only had been made only Maxwellian molecules, or, in a singular result of Villani, for super-hard collisions Recent work of myself, Carvalho and Loss extends this progress to the physically significant hard-sphere case, as will be explained in this lecture. I will also discuss recent results of Mischler and Mouhot on ropagation of chaos for this model that makes use of the new rate information.