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

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

2002-12-17

arxiv.org/abs/math-ph/0212050v1

J.Phys.A:Math.Gen. v.36 (2003), 4035-4047

Physics

Mathematical Physics

13 pages

Scientific paper

10.1088/0305-4470/36/14/308

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.

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