Concentration of permanent estimators for certain large matrices

Let An=(aij)ni,j=1 be an n.n positive matrix with entries in [a,b],0<a.b. Let Xn=(.aijxij)ni,j=1 be a random matrix, where {xij} are i.i.d. N(0,1) random variables. We show that for large n, det(XTnXn) concentrates sharply at the permanent of An, in the sense that n.1log(det(XTnXn)/perAn).n..0 in probability.