Real zeros of random algebraic polynomials with binomial elements
type: Item
instance of: scholarly article
title: Real zeros of random algebraic polynomials with binomial elements
zbMATH Open document ID: 1111.60034
DOI: 10.1155/JAMSA/2006/13980
author: Kambiz Farahmand
author: Ahmad Nezakati
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 2007-03-19T00:00:00Z
full work available at URL: https://eudml.org/doc/53099
review text: Summary: This paper provides an asymptotic estimate for the expected number of real zeros of a random algebraic polynomial \(a_0+a_1x+a_2 x^2+\cdots+a_{n-1}x^{n-1}\). The coefficients \(a_j\) \((j=0,1,2,\dots, n-1)\) are assumed to be independent normal random variables with mean zero. For integers \(m\) and \(k=O(\log n)^2\) the variances of the coefficients are assumed to have nonidentical value \(\text{var} (a_j)={k-1\choose j-ik}\), where \(n=k\cdot m\) and \(i=0,1,2,\dots,m-1\). Previous results are mainly for identically distributed coefficients or when \(\text{var} (a_j)= {n\choose j}\). We show that the latter is a special case of our general theorem.
Mathematics Subject Classification ID: 60G99
zbMATH DE Number: 5134599
MaRDI profile type: Publication
cites work: Real roots of random polynomials: universality close to accumulation points
cites work: Correlation between zeros of a random polynomial
cites work: Q4663134
cites work: Distribution of roots of random polynomials
cites work: Quantum chaotic dynamics and random polynomials
cites work: How many zeros of a random polynomial are real?
cites work: Q4265272
cites work: Algebraic polynomials with non-identical random coefficients
cites work: On the Expected Number of Real Zeros of Random Polynomials. II. Coefficients With Non-Zero Means
cites work: On the average number of real roots of a random algebraic equation
cites work: A note on the complex roots of complex random polynomials
cites work: Mathematical Analysis of Random Noise
cites work: Q3878478
Recommended article: Real Zeros of Random Algebraic Polynomials
Recommended article: Q4293654
Recommended article: Real zeros of classes of random algebraic polynomials
Recommended article: Real Zeros of Algebraic Polynomials with Dependent Random Coefficients
Recommended article: REAL ZEROS OF ALGEBRAIC POLYNOMIALS WITH STABLE RANDOM COEFFICIENTS
Recommended article: Q4731924
Recommended article: The real zeros of a random algebraic polynomial with dependent coefficients
Recommended article: Q3793459
Recommended article: Real almost zeros of random polynomials with complex coefficients
description: scientific article; zbMATH DE number 5134599