Statistical mechanics of Coulomb gases
A talk in the Keine Reihe series by
Sylvia Serfaty
| Abstract: | Large ensembles of points with Coulomb type interactions arise
in various settings of condensed matter physics, classical and quantum mechanics,
statistical mechanics, random matrices and even approximation theory, We study
the Gibbs measure associated to such systems in general dimension. We discuss
the free energy expansion as well as a description of the microscopic behavior of
the system as N tends to in nity via a Large Deviations Principle and a Central
Limit Theorem for
uctuations. This allows for instance to observe the e ect of the
temperature and to connect with crystallization questions. We will give an idea of
tools and methods used to prove the results, in particular the introduction of the
"electric formulation". |