Mesoscopic eigenvalue statistics of Wigner matrices
classification
🧮 math.PR
math-phmath.MP
keywords
eigenvaluemesoscopicscalesstatisticswignerconvergeeigenvaluesextent
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We prove that the linear statistics of the eigenvalues of a Wigner matrix converge to a universal Gaussian process on all mesoscopic spectral scales, i.e. scales larger than the typical eigenvalue spacing and smaller than the global extent of the spectrum.
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