Moderate deviations for the determinant of Wigner matrices

2013/01/14 by Döring, Hanna, Eichelsbacher, Peter
#15A18 #60B20 #60F10 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1301.2915

Abstract

We establish a moderate deviations principle (MDP) for the log-determinant log | det (M_n) | of a Wigner matrix M_n matching four moments with either the GUE or GOE ensemble. Further we establish Cramér--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.

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