A central limit theorem for the determinant of a Wigner matrix

摘要

We establish a central limit theorem for the log-determinant log{pipe}det(M _n){pipe} 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(logn!-12logn,12logn)R when one matches moments with GUE, and N(logn!-14logn,14logn)R when one matches moments with GOE.