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.
Gluing formulas for determinants of Dolbeault laplacians on Riemann surfaces
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abstract
We present gluing formulas for zeta regularized determinants of Dolbeault laplacians on Riemann surfaces. These are expressed in terms of determinants of associated operators on surfaces with boundary satisfying local elliptic boundary conditions. The conditions are defined using the additional structure of a framing, or trivialization of the bundle near the boundary. An application to the computation of bosonization constants follows directly from these formulas.
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2019 1verdicts
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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.