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Geometric and probabilistic aspects of Coulomb gases

Abstract : We explore probabilistic models usually called Coulomb gases. They arise naturally in mathematics and physics. We can mention random matrix theory, the Laughlin fractional quantum Hall effect and the Ginzburg-Landau systems of superconductivity. In order to better understand the role of the ambient space, we study geometric versions of such systems. We exploit three structures. The first one comes from the electrostatic nature of the interaction given by Gauss's law. The second one is the determinantal structure which appears only for a specific temperature. The third one is the minimization of the free energy principle, coming from physics which gives us a tool to understand more general models. This work leads to many open questions on a whole family of models which can be of independent interest.
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Contributor : David García Zelada Connect in order to contact the contributor
Submitted on : Thursday, March 5, 2020 - 1:23:45 PM
Last modification on : Wednesday, February 16, 2022 - 4:10:03 PM
Long-term archiving on: : Saturday, June 6, 2020 - 3:27:59 PM


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  • HAL Id : tel-02499570, version 1



David García-Zelada. Geometric and probabilistic aspects of Coulomb gases. Mathematical Physics [math-ph]. PSL Research University, 2019. English. ⟨tel-02499570⟩



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