Negative moments of characteristic polynomials of random 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 $N \to \infty$. The results agree nontrivially with a recent conjecture of Berry & 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. 
Yan V. Fyodorov and Jonathan P. Keating