Microscopic description of Coulomb gases

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.  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).