Universality at the Edge of the Spectrum¶in Wigner Random Matrices

Abstract:We prove universality at the edge for rescaled correlation functions of Wigner random matrices in the limit n→+∞. As a corollary, we show that, after proper rescaling, the 1th, 2nd, 3rd, etc. eigenvalues of Wigner random hermitian (resp. real symmetric) matrix weakly converge to the distributions established by Tracy and Widom in G.U.E. (G.O.E.) cases.

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