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We prove a Central Limit Theorem for the linear statistics of two-dimensional Coulomb gases, with arbitrary inverse temperature and general confining potential, at the macroscopic and mesoscopic scales and possibly near the boundary of the support of the equilibrium measure.
Potentiel d’équilibre et capacité des ensembles avec quelques applications à la théorie des fonctions
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L.A. Caffarelli and N.M. Riviere · 1976
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S. Sheffield · 2007
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Fluctuations of eigenvalues of random normal matrices
Y. Ameur, H. Hedenmalm, and N. Makarov · 2011
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Y. Ameur and J. Ortega-Cerdà · 2012
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Bulk universality of general β \beta -ensembles with non-convex potential
P. Bourgade, L. Erdös, and H.-T. Yau · 2012
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Regularity of free boundaries in obstacle-type problems
Incompressibility estimates for the laughlin phase
N. Rougerie and J. Yngvason · 2015
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S. Serfaty · 2015
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R. Bauerschmidt, P. Bourgade, M. Nikula, and H.-T. Yau · 2016
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Mesoscopic central limit theorem for general β \beta -ensembles
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