Negative moments of characteristic polynomials of random GOE matrices and singularity-dominated strong fluctuations
نویسندگان
چکیده
We calculate the negative integer moments of the (regularized) characteristic polynomials of N × N random matrices taken from the Gaussian Orthogonal Ensemble (GOE) in the limit as N → ∞. 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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