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

Yan V. Fyodorov·Jonathan P. Keating
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Abstract

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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Yan V. Fyodorov, Jonathan P. Keating. 2002-12-17. Negative moments of characteristic polynomials of random GOE matrices and singularity-dominated strong fluctuations. https://doi.org/10.1088/0305-4470%2F36%2F14%2F308

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