Laure Saint-Raymond (Paris)
From Newton's dynamics to the heat equation
The goal of this lecture is to show how the brownian motion can be derived
rigorously from a deterministic system of hard spheres in the limit where
the number of particles $N$ tends to infinity, and their diameter
simultaneously converges to 0.
As suggested by Hilbert in his sixth problem, we will use the linear
Boltzmann equation as an intermediate level of description for the
dynamics of one tagged particle.
We will discuss especially the origine of irreversibility, which is a
fundamental feature of both the brownian motion and the Boltzmann equation
having no counterpart at the microscopic level.