✦ LIBER ✦
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
No coin nor oath required. For personal study only.
✦ 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.