A central limit theorem for the determinant of a Wigner matrix

Abstract

We establish a central limit theorem for the log-determinant $\log |\det (M_n)|$ of a Wigner matrix $M_n$, under the assumption of four matching moments with either the GUE or GOE ensemble. More specifically, we show that this log-determinant is asymptotically distributed like $N(\log \sqrt{n!}-1/2\log n,1/2\log n{)}_{\mathbb{R}}$ when one matches moments with GUE, and $N(\log \sqrt{n!}-1/4\log n,1/4\log n{)}_{\mathbb{R}}$ when one matches moments with GOE.

29 pages, no figures, to appear, Adv. Math.. This is the final version

References in corpus (2)

• Local semicircle law and complete delocalization for Wigner random matrices
• Asymptotic behavior of random determinants in the Laguerre, Gram and Jacobi ensembles

Cited by in corpus (1)

• Central limit theorem for partial linear eigenvalue statistics of Wigner matrices