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.
|Translated title of the contribution||Negative moments of characteristic polynomials of GOE matrices and singularity-dominated strong fluctuations|
|Pages (from-to)||4035 - 4046|
|Journal||Journal of Physics A: Mathematical and General|
|Publication status||Published - 11 Apr 2003|
Bibliographical notePublisher: IOP Publishing Ltd
Other identifier: IDS number 674GG