Integrable random matrix ensembles

Abstract

We propose new classes of random matrix ensembles whose statistical properties are intermediate between statistics of Wigner-Dyson random matrices and Poisson statistics. The construction is based on integrable N-body classical systems with a random distribution of momenta and coordinates of the particles. The Lax matrices of these systems yield random matrix ensembles whose joint distribution of eigenvalues can be calculated analytically thanks to integrability of the underlying system. Formulas for spacing distributions and level compressibility are obtained for various instances of such ensembles.

32 pages, 8 figures

References in corpus (1)

• Perturbation approach to multifractal dimensions for certain critical random matrix ensembles

Cited by in corpus (19)

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• Integrable many-body systems of Calogero-Ruijsenaars type
• Level compressibility of certain random unitary matrices
• Crystalline Spectral Form Factors