  Let A_n=(a_{ij})_{i,j=1}^n be an n\times n positive matrix with entries in
[a,b], 0<a\le b. Let X_n=(\sqrta_{ij}x_{ij})_{i,j=1}^n be a random matrix,
where {x_{ij}} are i.i.d. N(0,1) random variables. We show that for large n,
\det (X_n^TX_n) concentrates sharply at the permanent of A_n, in the sense that
n^{-1}\log (\det(X_n^TX_n)/perA_n)\to_{n\to\infty}0 in probability.
