Crystallization of random trigonometric polynomials
Mathematical Physics
2009-11-11 v1 Complex Variables
math.MP
Probability
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.
Cite
@article{arxiv.math-ph/0601007,
title = {Crystallization of random trigonometric polynomials},
author = {David W. Farmer and Mark Yerrington},
journal= {arXiv preprint arXiv:math-ph/0601007},
year = {2009}
}
Comments
10 pages, 3 figures