Moderate deviations for the determinant of Wigner matrices
Probability
2013-01-16 v2
Abstract
We establish a moderate deviations principle (MDP) for the log-determinant of a Wigner matrix matching four moments with either the GUE or GOE ensemble. Further we establish Cram\'er--type moderate deviations and Berry-Esseen bounds for the log-determinant for the GUE and GOE ensembles as well as for non-symmetric and non-Hermitian Gaussian random matrices (Ginibre ensembles), respectively.
Keywords
Cite
@article{arxiv.1301.2915,
title = {Moderate deviations for the determinant of Wigner matrices},
author = {Hanna Döring and Peter Eichelsbacher},
journal= {arXiv preprint arXiv:1301.2915},
year = {2013}
}
Comments
20 pages, one missing reference added; Limit Theorems in Probability, Statistics and Number Theory, Springer Proceedings in Mathematics and Statistics, 2013