Journal of Statistical Physics

, Volume 123, Issue 6, pp 1219–1230 | Cite as

Crystallization of Random Trigonometric Polynomials

  • David W. Farmer
  • Mark Yerrington


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.

Random polynomial crystallization pair correlation of zeros 


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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.American Institute of MathematicsPalo AltoUSA

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