Universality of the local spacing distribution in certain ensembles of Hermitian Wigner matrices. (English) Zbl 0978.15020

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.


15B52 Random matrices (algebraic aspects)
60J65 Brownian motion
15A18 Eigenvalues, singular values, and eigenvectors
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