Universality of the local spacing distribution in certain ensembles of Hermitian Wigner matrices
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.
scientific article; zbMATH DE number 1631876