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Complex Zeros of Trigonometric Polynomials with Standard Normal Random Coefficients

✍ Scribed by K. Farahmand; A. Grigorash


Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
94 KB
Volume
262
Category
Article
ISSN
0022-247X

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✦ Synopsis


In this paper, we obtain an exact formula for the average density of the distribution of complex zeros of a random trigonometric polynomial

, where the coefficients η j = a j + ιb j , and a j n j=1 and b j n j=1 are sequences of independent normally distributed random variables with mean 0 and variance 1. We also provide the limiting behaviour of the zeros density function as n tends to infinity. The corresponding results for the case of random algebraic polynomials are known.