The Wigner-Dyson-Mehta Bulk Universality Conjecture for Wigner Matrices
The Wigner-Dyson-Mehta Bulk Universality Conjecture for Wigner Matrices
A well known conjecture of Wigner, Dyson, and Mehta asserts that the (appropriately normalized) $k$-point correlation functions of the eigenvalues of random $n \times n$ Wigner matrices in the bulk of the spectrum converge (in various senses) to the $k$-point correlation function of the Dyson sine process in the asymptotic …