Search results for "Wigner matrices"

On Non-Gaussian limiting laws for certain statistics of Wigner Matrices

2013

This paper is a continuation of our papers [12-14] in which the limiting laws of fluctuations were found for the linear eigenvalue statistics Tr j(M(n)) and for the normalized matrix elements √n̅jjj(M(n)) of differentiable functions of real symmetric Wigner matrices M(n) as n →∞. Here we consider another spectral characteristic of Wigner matrices, xnA [j] = Tr j(M(n))A(n), where {A(n)}∞n=1 is a certain sequence of non-random matrices. We show first that if M(n) belongs to the Gaussian Orthogonal Ensemble, then xnA [j] satisfies the Central Limit Theorem. Then we consider Wigner matrices with i.i.d. entries possessing the entire characteristic function and find the limiting probability law f…