Title: Microscopic description of Coulomb-type systems

Abstract:
We are interested in systems of points with Coulomb, logarithmic or more
generally Riesz interactions (i.e. inverse powers of the distance). They
arise in various settings: an instance is the classical Coulomb gas which
in some cases happens to be a random matrix ensemble, another is vortices
in the Ginzburg-Landau model of superconductivity, where one observes in
certain regimes the emergence of densely packed point vortices forming
perfect triangular lattice patterns named Abrikosov lattices, a third is
the study of Fekete points which arise in approximation theory.
After reviewing the motivations, we will take a point of view based on the
detailed expansion of the interaction energy to describe the microscopic
behavior of the systems. In particular a Central Limit Theorem for
fluctuations and a Large Deviations Principle for the microscopic point
processes are given.
This allows to observe the effect of  the temperature as it gets very
large or very small, and to connect with crystallization questions.
The main results are joint with Thomas Lebl\’e and also based on previous
works with Etienne Sandier, Nicolas Rougerie and Mircea Petrache.

Wednesday, October 26, 4:30 – 5:30 p.m.
Mathematics 520
Tea will be served at 4:00 p.m.

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