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(14:00-15:00 UTC) Speaker: Thomas Leblé (CNRS - Université de Paris (MAP5))
Title: Coulomb gases: a short introduction
Abstract: Coulomb potentials are natural examples of systems with long-range interactions. They appear in statistical physics, random matrix theory, vortex systems, constructive approximation… and can be seen as a (possibly infinite) random collection of points that exhibit interesting stochastic features depending on the length scale and the temperature T.
For example, their global arrangement is predicted by a mean field model and is found to be independent of T, whereas their local arrangement varies wildly with T while conserving strong, surprising rigidity properties all along.
I will present some basic facts about the analysis of Coulomb gases and mention a few long-standing questions around which recent developments have taken place.
(15:00-16:00 UTC) Sylvia Serfaty (NYU Courant)
Title: Local laws and fluctuations for Coulomb gases
Abstract: We are interested in the statistical mechanics of systems of N points with Coulomb interactions in general dimension for a broad temperature range. We discuss local laws characterizing the rigidity of the system at the microscopic level, as well as free energy expansion and Central Limit Theorems for fluctuations.
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We hope to see you all tomorrow!
One World Probability Team