Edge fluctuations of eigenvalues of Wigner matrices
Probability
2013-01-12 v2
Abstract
We establish a moderate deviation principle (MDP) for the number of eigenvalues of a Wigner matrix in an interval close to the edge of the spectrum. Moreover we prove a MDP for the th largest eigenvalue close to the edge. The proof relies on fine asymptotics of the variance of the eigenvalue counting function of GUE matrices due to Gustavsson. The extension to large families of Wigner matrices is based on the Tao and Vu Four Moment Theorem. Possible extensions to other random matrix ensembles are commented.
Keywords
Cite
@article{arxiv.1203.2115,
title = {Edge fluctuations of eigenvalues of Wigner matrices},
author = {Hanna Döring and Peter Eichelsbacher},
journal= {arXiv preprint arXiv:1203.2115},
year = {2013}
}
Comments
16 pages, some minor corrections. arXiv admin note: text overlap with arXiv:1104.0221