Crystallization of Random Trigonometric Polynomials |
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Authors: | David W. Farmer Mark Yerrington |
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Affiliation: | (1) American Institute of Mathematics, Palo Alto, USA |
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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. |
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Keywords: | Random polynomial crystallization pair correlation of zeros |
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