Johansson, Kurt Universality of the local spacing distribution in certain ensembles of Hermitian Wigner matrices. (English) Zbl 0978.15020 Commun. Math. Phys. 215, No. 3, 683-705 (2001). The author considers the distribution of the distances between adjacent eigenvalues for Hermitian random matrices with independent entries. It is conjectured that this generally is the same as with the Gaussian unitary ensemble. Theorem 1.3 shows this is true for a class \(W^p_a\) involving convolutions of a fixed Gaussian density with a distribution having finite moments, fixed variance and varying with the different entries. Results on Brownian motion are used in the proof. Reviewer: Kim Hang Kim (Montgomery) Cited in 103 Documents MSC: 15B52 Random matrices (algebraic aspects) 60J65 Brownian motion 15A18 Eigenvalues, singular values, and eigenvectors Keywords:eigenvalues of random matrix; Hermitian Wigner matrix; Gaussian unitary ensemble; Brownian motion; local spacing distribution × Cite Format Result Cite Review PDF Full Text: DOI arXiv