A central limit theorem for the determinant of a Wigner matrix

We establish a central limit theorem for the log-determinant log|det(Mn)|log|det(Mn)| of a Wigner matrix MnMn, 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(logn!−12logn,12logn)R when one matches moments with GUE, and N(logn!−14logn,14logn)R when one matches moments with GOE.