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Tuesday, August 20, 2019 - 09:30 in ZiF

Statistical mechanics of Coulomb gases

A talk in the Summer School Randomness in Physics & Mathematics 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".


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