Crystallization of random trigonometric polynomials

Details Crystallization of random trigonometric polynomials Crystallization of random trigonometric polynomials

2006-01-04

arxiv.org/abs/math-ph/0601007v1

Physics

Mathematical Physics

10 pages, 3 figures

Scientific paper

10.1007/s10955-006-9126-7

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.

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