Universality at the edge of the spectrum in Wigner random matrices
Mathematical Physics
2009-10-31 v2 math.MP
Probability
Abstract
We prove universality at the edge for rescaled correlation functions of Wigner random matrices in the limit . 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.
Keywords
Cite
@article{arxiv.math-ph/9907013,
title = {Universality at the edge of the spectrum in Wigner random matrices},
author = {Alexander Soshnikov},
journal= {arXiv preprint arXiv:math-ph/9907013},
year = {2009}
}
Comments
We corrected several misprints and little mistakes (the most important one is formula (1.15)). We also reformulated two auxiliary theorems (Theorem 2 and Theorem 3) to emphasize the asymptotic nature of the results