Panorama of Mathematics - Laure Saint-Raymond

Explore the fascinating world of particle dynamics in this 52-minute lecture by Laure Saint-Raymond titled "Exchangeability, chaos and dissipation in large systems of particles." Delve into the complexities of hard sphere dynamics, predictability in particle systems, and the concepts of ergodicity and invariant measures. Examine the role of entropy and chaos in large particle systems, and understand the mean field limit and its convergence to the Boltzmann equation. Investigate the low density limit, propagation of chaos, and fluctuations in particle systems. Analyze the relationships between correlations, dissipation, and mixing mechanisms. This talk, part of the "Panorama of Mathematics" conference organized by the Hausdorff Center for Mathematics, offers a comprehensive overview of current trends, results, and challenges in the mathematical sciences related to large-scale particle systems.

Intro
The hard sphere dynamics
What can be predicted?
Ergodicity and invariant measures
Concentration of measure
Entropy and chaos
The mean field limit
Convergence to the Boltzmann equation
The low density limit
Propagation of chaos
Fluctuations
Correlations and dissipation
Mixing mechanisms