CLT for Circular beta-Ensembles at high temperature
نویسندگان
چکیده
We consider the macroscopic large N limit of Circular beta-Ensemble at high temperature, and its weighted version as well, in regime where inverse temperature scales β/N for some parameter β>0. More precisely, N→∞, equilibrium measure this particle system is described unique minimizer a functional which interpolates between relative entropy (β=0) logarithmic energy (β=∞). The purpose work to show that fluctuation empirical around converges towards Gaussian field whose covariance structure Lebesgue L2 Sobolev H1/2 (β=∞) norms. furthermore obtain rate convergence fluctuations W2 metric. Our proof uses normal approximation result Lambert et al. [24], Coulomb transport inequality Chafaï [8], spectral analysis operator associated with limiting structure.
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2021
ISSN: ['0022-1236', '1096-0783']
DOI: https://doi.org/10.1016/j.jfa.2020.108869