On correlation function of high moments of Wigner random matrices
Mathematical Physics
2013-09-09 v3 math.MP
Probability
Abstract
We consider the Wigner ensemble of Hermitian n-dimensional random matrices and study the correlation function K(s',s") of their moments in the limit when the numbers s', s" of the moments are proportional to n to the power 2/3. We show that the limiting expression of K does not depend on the moments of the random matrix elements. The proof is based on a combination of the arguments by Ya. Sinai and A. Soshnikov with the detailed study of a moment analog of the Inverse Participation Ratio of the Gaussian Unitary Invariant Ensemble (GUE).
Keywords
Cite
@article{arxiv.1011.3965,
title = {On correlation function of high moments of Wigner random matrices},
author = {Oleksiy Khorunzhiy},
journal= {arXiv preprint arXiv:1011.3965},
year = {2013}
}
Comments
Minor changes; final version to appear in Random Oper. Stochastic Equations