Sobolev convergence of log-determinants for smooth Wigner matrices
classification
🧮 math.PR
math-phmath.MP
keywords
matricessmoothsobolevwignercenteredconvergeconvergencecorrelated
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We show that the fields emerging from the log-determinant and the eigenvalue counting function of smooth Wigner matrices converge in law to centered Gaussian, logarithmically correlated, random elements in every negative Sobolev space $H^{-s}$.
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