English

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 logdet(Mn)\log | \det (M_n) | of a Wigner matrix MnM_n 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

R2 v1 2026-06-21T23:08:46.373Z