The average number of real zeros of a random trigonometric polynomial-Reference-Cited by-同舟云学术

The average number of real zeros of a random trigonometric polynomial

Published:1968-07 Issue:3 Volume:64 Page:721-730
ISSN:0305-0041
Container-title:Mathematical Proceedings of the Cambridge Philosophical Society
language:en
Short-container-title:Math. Proc. Camb. Phil. Soc.

Author:

Das Minaketan

Abstract

AbstractLet a1, a2,… be a sequence of mutually independent, normally distributed, random variables with mathematical expectation zero and variance unity; let b1, b2,… be a set of positive constants. In this work, we obtain the average number of zeros in the interval (0, 2π) of trigonometric polynomials of the form

for large n. The case when bk = kσ (σ > − 3/2;) is studied in detail. Here the required average is (2σ + 1/2σ + 3)½.2n + o(n) for σ ≥ − ½ and of order n3/2; + σ in the remaining cases.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference5 articles.

1. (2) Das M. The number of real zeros of certain random trigonometric polynomials—submitted to Math. Student.

2. The Number of Real Zeros of a Random Trigonometric Polynomial

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