Random matrices: Law of the determinant

Let An be an n by n random matrix whose entries are independent real random variables with mean zero, variance one and with subexponential tail. We show that the logarithm of |detAn| satisfies a central limit theorem. More precisely, supx.R...P(log(|detAn|).(1/2)log(n.1)!.(1/2)logn.x).P(N(0, 1).x)....log.1/3+o(1)n.