Modul:   MAT673  Seminar PDE and Mathematical Physics

The correlation error in the Boltzmann--Grad limit

Talk by Dr. Sergio Simonella

Speaker invited by: Prof. Dr. Benjamin Schlein

Date: 14.04.14  Time: 17.15 - 19.00  Room: Y27H25

We present a quantitative analysis of the Boltzmann--Grad (low--density) limit of a hard sphere system. We introduce and study a set of functions (correlation errors) measuring the deviations in time from the statistical independence of particles (propagation of chaos). In the context of the BBGKY hierarchy, a correlation error of order $k$ measures the event where $k$ tagged particles form a recolliding group. We prove that, provided $k$ is not too large, such an error flows to zero with the hard spheres diameter $\e$, for short times, as $\e^{\g k}$, for some $\g\in(0,1)$. This requires a new analysis on multiple recollisions, and improves previous estimates on high order correlation functions. (Joint work with M. Pulvirenti.)