Propagation of chaos and irreversibility for systems of particles in the low density limit

Prof. Laure Saint-Raymond (ENS, Paris)

December 05, 2013, 15:15 - 17:00, HG G 19.2
December 06, 2013, 10:15 - 12:00, HG G 43
December 19, 2013, 15:15 - 17:00, HG G 19.2
December 20, 2013, 10:15 - 12:00, HG G 43

Abstract

The goal of this series of lectures is to show how the Boltzmann equation can be derived rigorously from a deterministic system of interacting particles in the limit where the number of particles N tends to infinity, and their diameter simultaneously converges to 0. We will discuss especially the origin of irreversibility, which is a fundamental feature of  the Boltzmann equation having no counterpart at the microscopic level.

Lecture 1: the BBGKY hierarchy and its formal low density limit
- a statistical description of large systems of particles
- the BBGKY hierarchy and collision trees
- the low density limit and the chaos assumption

Lecture 2: Control of recollisions
- pseudo-trajectories
- basic geometric lemma
- an iterative construction of "good configurations"

Lecture 3: Control of large collision trees (1)
- ensembles in statistical physics, and functional spaces
- loss continuity estimates and the Cauchy-Kowalewski theory
- a short time convergence result

Lecture 4: Control of large collision trees (2)
- a long time convergence result in linear regime
- collision trees with super exponential growth
- concluding remarks and perspectives