Random polynomials, random matrices, and $L$-functions

Abstract

We show that the Circular Orthogonal Ensemble of random matrices arises naturally from a family of random polynomials. This sheds light on the appearance of random matrix statistics in the zeros of the Riemann zeta-function.

arXiv commentAdded background material. Final version. To appear in Nonlinearity

References in corpus (1)

• Quantum Chaotic Dynamics and Random Polynomials

Cited by in corpus (1)

• Randomly incomplete spectra and intermediate statistics