Crystallization of random trigonometric polynomials
数学物理
2009-11-11 v1 复变函数
math.MP
概率论
摘要
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.
引用
@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}
}
备注
10 pages, 3 figures