Fluctuating Boltzmann equation and large deviations for a hard sphere gas

Abstract: A gas dynamics can be modelled by a billiard made of hard spheres, moving according to the laws of classical mechanics. Initially the spheres are randomly distributed according to a probability measure which is then transported by the flow of the deterministic dynamics. Since the seminal work of Lanford, it is known in the kinetic limit that the gas density converges towards the Boltzmann equation (at least for a short time).

In this talk, we are going to discuss the fluctuations of the microscopic dynamics around the Boltzmann equation and the convergence of the fluctuation field to the fluctuating Boltzmann equation. We will also show that the occurence of atypical evolutions can be quantified by a large deviation principle. This analysis relies on the study of the correlations created by the Hamiltonian dynamics. We will see that the emergence of irreversibility in the kinetic limit can be related to the singularity of these correlations.

mathematical physicsprobability

Audience: researchers in the topic

Comments: Zoom meeting ID: 991 4448 8133, password: 800920

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Probability and the City Seminar

Series comments: The Probability and the City Seminar is organized jointly by the probability groups of Columbia University and New York University.

Video recordings of talks are posted online at www.youtube.com/channel/UC0CXjG-ZSIZHy0S40Px2FEQ .

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