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Matrix models for circular ensembles
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Matrix models for circular ensembles
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We describe an ensemble of (sparse) random matrices whose eigenvalues follow the Gibbs distribution for n particles of the Coulomb gas on the unit circle at inverse temperature beta. Our approach combines elements from the theory of orthogonal polynomials on the unit circle with ideas from recent work of Dumitriu and Edelman. In particular, we resolve a question left open by them: find a tri-diagonal model for the Jacobi ensemble.
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Crystalline Spectral Form Factors
Strong level repulsion produces damped crystalline oscillations of the spectral form factor, with a Debye-Waller suppression, a new plateau time scale t* ≈ t_H sqrt(β/4), and predictable derivative singularities.
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