On Non-Gaussian Limiting Laws for the Certain Statistics of the Wigner Matrices

Details On Non-Gaussian Limiting Laws for the Certain Statistics of the Wigner Matrices On Non-Gaussian Limiting Laws for the Certain Statistics of the Wigner Matrices

2012-01-14

arxiv.org/abs/1201.3027v1

Physics

Mathematical Physics

arXiv admin note: text overlap with arXiv:1103.2345

Scientific paper

We continue investigations of our previous papers, in which there were proved central limit theorems (CLT) for linear eigenvalue statistics Tr f(M_n) and there were found the limiting probability laws for the normalised matrix elements of differential functions f(M_n) of nxn real symmetric Wigner matrices M_n. Here we consider another spectral characteristic of Wigner matrices, namely, Tr f(M_n)A_n, where {A_n, n=1,2,...} is a certain sequence of non-random matrices. We show first that if M_n belongs to the Gaussian Orthogonal Ensemble, then Tr f(M_n)A_n satisfies CLT. Then we consider Wigner matrices with i.i.d. entries possessing entire characteristic function and find the limiting probability law for Tr f(M_n)A_n, which in general is not Gaussian.

Affiliated with

Also associated with

No associations

Rating

On Non-Gaussian Limiting Laws for the Certain Statistics of the Wigner Matrices does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On Non-Gaussian Limiting Laws for the Certain Statistics of the Wigner Matrices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Non-Gaussian Limiting Laws for the Certain Statistics of the Wigner Matrices will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-694123