Fluctuations of Two Dimensional Coulomb Gases

• Published in: Geometric and functional analysis Vol. 28; no. 2; pp. 443 - 508
• Main Authors: Leblé, Thomas, Serfaty, Sylvia
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.04.2018; Springer Nature B.V
• Subjects: Analysis; Confining; Convergence; Mathematics; Mathematics and Statistics; Upper bounds; Variation; Linear statistics; 82B05; Log gas; 60B10; 60B20; Ginibre ensemble; Gaussian free field; Coulomb gas; Central Limit Theorem; 60K35; 60F05; 60G15; ensembles

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. This can be stated in te...