Gaussian Fluctuations of Eigenvalues in Wigner Random Matrices

Details Gaussian Fluctuations of Eigenvalues in Wigner Random Matrices Gaussian Fluctuations of Eigenvalues in Wigner Random Matrices

2009-09-15

arxiv.org/abs/0909.2677v3

J. Stat. Phys., Volume 138, Number 6, (2010) 1045-1066

Mathematics

Probability

21 pages, to appear, J. Stat. Phys. References and other corrections suggested by the referees have been incorporated

Scientific paper

10.1007/s10955-009-9906-y

We study the fluctuations of eigenvalues from a class of Wigner random matrices that generalize the Gaussian orthogonal ensemble. We begin by considering an $n \times n$ matrix from the Gaussian orthogonal ensemble (GOE) or Gaussian symplectic ensemble (GSE) and let $x_k$ denote eigenvalue number $k$. Under the condition that both $k$ and $n-k$ tend to infinity with $n$, we show that $x_k$ is normally distributed in the limit. We also consider the joint limit distribution of $m$ eigenvalues from the GOE or GSE with similar conditions on the indices. The result is an $m$-dimensional normal distribution. Using a recent universality result by Tao and Vu, we extend our results to a class of Wigner real symmetric matrices with non-Gaussian entries that have an exponentially decaying distribution and whose first four moments match the Gaussian moments.

Affiliated with

Also associated with

No associations

Rating

Gaussian Fluctuations of Eigenvalues in Wigner Random 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 Gaussian Fluctuations of Eigenvalues in Wigner Random Matrices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Gaussian Fluctuations of Eigenvalues in Wigner Random Matrices will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-555026