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arXiv · 1906.08529

Sharp deviation inequalities for the 2D Coulomb gas and Quantum hall states, I

Robert J. Berman
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Abstract

We establish sharp deviation inequalities for the linear statistics of the 2D Coulomb gas. These imply sub-Gaussian inequalities, where the variance is given by the Dirichlet norm. The proofs use complex geometry and potential theory on Riemann surfaces and apply more generally to beta-ensembles, which also include integer Quantum Hall states on Riemann surfaces. In a sequel of the paper we give applications to large and moderate deviation principles, local laws at mesoscopic scales, quantitative Bergman kernel asymptotics. In a series of companion papers applications to concentration of measure, Monte-Carlo methods for numerical integration and random matrices are given and relations to Kahler geometry are explored.

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Robert J. Berman. 2019-06-20. Sharp deviation inequalities for the 2D Coulomb gas and Quantum hall states, I. https://arxiv.org/abs/1906.08529

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