Expected number of real zeros of random hyperbolic polynomial

If g 1, g 2,…, g n are independent, normally distributed random variables with mean zero and variance one, then the expected number of zeros of a polynomial of the form g 1 cosh t+g 2 cosh 2t+g 3 cosh 3t+⋯+g n cosh nt , for large values of n, is 1 π log n+C+ o(1) where C=0.038… .

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Bibliographic Details
Published in	Statistics & probability letters Vol. 70; no. 1; pp. 11 - 18
Main Author	Mahanti, Mina Ketan
Format	Journal Article
Language	English
Published	Amsterdam Elsevier B.V 15.10.2004 Elsevier
Series	Statistics & Probability Letters
Subjects	Exact sciences and technology Expected number of zeros Mathematical analysis Mathematics Probability and statistics Probability theory and stochastic processes Random polynomial Random polynomial Expected number of zeros Real functions Sciences and techniques of general use Stochastic analysis Expected number of zeros primary 60H99 Random polynomial secondary 26c99 Statistical method Gaussian distribution Mean estimation Probability theory
Online Access	Get full text
ISSN	0167-7152 1879-2103
DOI	10.1016/j.spl.2004.06.017

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Summary:	If g 1, g 2,…, g n are independent, normally distributed random variables with mean zero and variance one, then the expected number of zeros of a polynomial of the form g 1 cosh t+g 2 cosh 2t+g 3 cosh 3t+⋯+g n cosh nt , for large values of n, is 1 π log n+C+ o(1) where C=0.038… .
ISSN:	0167-7152 1879-2103
DOI:	10.1016/j.spl.2004.06.017