EVENT DETAILS AND ABSTRACT

Title: Microscopic Description of Coulomb-type Systems, Part II
Speaker: Sylvia Serfaty
Speaker Info: New York University
Brief Description:
Special Note: Open to registered participants only (http://sites.math.northwestern.edu/mwp)
Abstract:

We are interested in the statistical mechanics of systems of points with Coulomb, logarithmic or more generally Riesz interactions (i.e. inverse powers of the distance), at arbitrary temperature. A particular instance is the famous Ginibre ensemble in random matrices. 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, local laws on the energy and number of points, 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. This is based on works with Thomas Leblé and Scott Armstrong (themselves based on prior works with Etienne Sandier, Nicolas Rougerie and Mircea Petrache).