Explicit formulas for the distribution of complex zeros of a family of random sums

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:444

Article

Ledoan, Andrew¹ 

[1] Univ Tennessee, Dept Math, 415 EMCS Bldg,Dept 6956,615 McCallie Ave, Chattanooga, TN 37403 USA

关键词: Cholesky factorization;    Expected number of zeros;    Explicit formula;    Random sum;   

DOI  :  10.1016/j.jmaa.2016.07.015

来源: Elsevier

【 摘 要 】

The present paper provides an explicit formula for the average intensity of the distribution of complex zeros of a family of random sums of the form S-n(z) = Sigma(n)(j=0) eta(j)f(j)(z), where z is the complex variable x + iy, eta(j) = alpha(j) + i beta(j) and {alpha(j)}(j=0)(n) and {beta(j)}(j=0)(n) are sequences of standard normal independent random variables, and {f(j)}(j=0)(n) is a sequence of given analytic functions that are real-valued on the real number line. In addition, the numerical computations of the intensity functions and the empirical distributions for the special cases of random Weyl polynomials, random Taylor polynomials and random truncated Fourier cosine series are included as examples. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free