Gaussian fluctuations of eigenvalues in the GUE
Abstract
Under certain conditions on k we calculate the limit distribution of the k:th largest eigenvalue, xk, of the Gaussian Unitary Ensemble (GUE). More specifically, if n is the dimension of a random matrix from the GUE and k is such that both k and n-k tends to infinity as n tends to infinity then xk is normally distributed in the limit. We also consider the joint limit distribution of xk1 < ... < xkm where we require that k1, ki+1-ki and n-km, i=1..m-1, tends to infinity with n. The result is an m-dimensional Normal Distribution.
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