Universality at the edge of the spectrum in Wigner random matrices

Details Universality at the edge of the spectrum in Wigner random matrices Universality at the edge of the spectrum in Wigner random matrices

1999-07-15

arxiv.org/abs/math-ph/9907013v2

Commun. Math. Phys. v.207, 697-733 (1999)

Physics

Mathematical Physics

We corrected several misprints and little mistakes (the most important one is formula (1.15)). We also reformulated two auxili

Scientific paper

10.1007/s002200050743

We prove universality at the edge for rescaled correlation functions of
Wigner random matrices in the limit $n\to +\infty$. As a corollary, we show
that, after proper rescaling, the 1st, 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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