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

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.

arXiv comment13 pages

References in corpus (8)

• Negative moments of characteristic polynomials of random matrices: Ingham-Siegel integral as an alternative to Hubbard-Stratonovich transformation
• Replica Limit of the Toda Lattice Equation
• Replica field theories, Painleve transcendents, and exact correlation functions
• Characteristic polynomials of real symmetric random matrices
• Orbit bifurcations and the scarring of wavefunctions
• Characteristic polynomials of random Hermitian matrices and Duistermaat-Heckman localisation on non-compact Kaehler manifolds
• Energy conditions and classical scalar fields
• Moments of the characteristic polynomial in the three ensembles of random matrices

Cited by in corpus (12)

• On the averages of characteristic polynomials from classical groups
• Universal Results for Correlations of Characteristic Polynomials: Riemann-Hilbert Approach
• Singularity dominated strong fluctuations for some random matrix averages
• On Random Matrix Averages Involving Half-Integer Powers of GOE Characteristic Polynomials
• On the asymptotics of some large Hankel determinants generated by Fisher-Hartwig symbols defined on the real line
• A Fuchsian matrix differential equation for Selberg correlation integrals
• On the correlation functions of the characteristic polynomials of the sparse hermitian random matrices
• The Calogero-Moser equation system and the ensemble average in the Gaussian ensembles
• On the moments of characteristic polynomials
• Survival Probability of a Doorway State in regular and chaotic environments
• Integrability of zero-dimensional replica field theories at beta=1
• Tuck's incompressibility function: statistics for zeta zeros and eigenvalues