The scaled fluctuations of the Circular beta-Ensemble at inverse temperature beta/N converge to a Gaussian process with variance <psi, L^{-1} psi>_H, interpolating from the L2 norm to the H^{1/2} norm.
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CLT for Circular beta-Ensembles at High Temperature
The scaled fluctuations of the Circular beta-Ensemble at inverse temperature beta/N converge to a Gaussian process with variance <psi, L^{-1} psi>_H, interpolating from the L2 norm to the H^{1/2} norm.