Crystallization of random trigonometric polynomials

Abstract

We give a precise measure of the rate at which repeated differentiation of a random trigonometric polynomial causes the roots of the function to approach equal spacing. This can be viewed as a toy model of crystallization in one dimension. In particular we determine the asymptotics of the distribution of the roots around the crystalline configuration and find that the distribution is not Gaussian.

10 pages, 3 figures

References in corpus (1)

• Quantum Chaotic Dynamics and Random Polynomials

Cited by in corpus (1)

• On the critical points of random matrix characteristic polynomials and of the Riemann $\xi$-function