Negative moments of characteristic polynomials of GOE matrices and singularity-dominated strong fluctuations

We calculate the negative integer moments of the (regularized) characteristic polynomials of N x N random matrices taken from the Gaussian orthogonal ensemble (GOE) in the limit as N --> infinity. The results agree nontrivially with a recent conjecture of Berry and Keating motivated by techniques developed in the theory of singularity-dominated strong fluctuations. This is the first example where nontrivial predictions obtained using these techniques have been proved.