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Fluctuations of eigenvector overlaps and the Berry conjecture for Wigner matrices
Published 20 Dec 2022 in math.PR, math-ph, and math.MP | (2212.10694v1)
Abstract: We prove that any finite collection of quadratic forms (overlaps) of general deterministic matrices and eigenvectors of an $N\times N$ Wigner matrix has joint Gaussian fluctuations. This can be viewed as the random matrix analogue of the Berry random wave conjecture.
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