Fluctuations of eigenvector overlaps and the Berry conjecture for Wigner matrices

2022/12/20 by Lucas Benigni, Benigni, Lucas, Giorgio Cipolloni +1 · 1 citation
Mathematics · #15B52 #60B20 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2212.10694

openalex publication_date 2022/12/20 · openalex created_date 2023/01/04 · openalex updated_date 2026/07/28

Abstract

We prove that any finite collection of quadratic forms (overlaps) of general deterministic matrices and eigenvectors of an N× N Wigner matrix has joint Gaussian fluctuations. This can be viewed as the random matrix analogue of the Berry random wave conjecture.

Cited by

• Convergence of local eigenvector processes of generalized Wigner matrices

Related

• Normal fluctuation in quantum ergodicity for Wigner matrices
• Fluctuations of Eigenvalues for Generalized Patterned Gaussian Random Matrices
• Three-dimensional Gaussian fluctuations of spectra of overlapping stochastic Wishart matrices
• Edge fluctuations of eigenvalues of Wigner matrices
• Joint Global Fluctuations of complex Wigner and deterministic Matrices