Sharp deviation inequalities are proved for linear statistics of the 2D Coulomb gas using complex geometry and potential theory on Riemann surfaces, extending to beta-ensembles and quantum Hall states.
Landkof, Foundations of Modern Potential Theor y , Grundlehren der Math- ematischen Wis- senschaften, 180 0 Springer-Verlag, Berlin, (1972)
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Sharp deviation inequalities for the 2D Coulomb gas and Quantum hall states, I
Sharp deviation inequalities are proved for linear statistics of the 2D Coulomb gas using complex geometry and potential theory on Riemann surfaces, extending to beta-ensembles and quantum Hall states.