Universality of the local spacing distribution in certain ensembles of hermitian Wigner matrices

Details Universality of the local spacing distribution in certain ensembles of hermitian Wigner matrices Universality of the local spacing distribution in certain ensembles of hermitian Wigner matrices

2000-06-21

arxiv.org/abs/math-ph/0006020v1

Physics

Mathematical Physics

21 pages

Scientific paper

10.1007/s002200000328

Consider an $N\times N$ hermitian random matrix with independent entries, not necessarily Gaussian, a so called Wigner matrix. It has been conjectured that the local spacing distribution, i.e. the distribution of the distance between nearest neighbour eigenvalues in some part of the spectrum is, in the limit as $N\to\infty$, the same as that of hermitian random matrices from GUE. We prove this conjecture for a certain subclass of hermitian Wigner matrices.

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