Real zeros of algebraic polynomials with nonidentical dependent random coefficients

2019/09/20 by Sabita Sahoo, Sahoo, Sabita, Partiswari Maharana +1
Mathematics · #Analytic and geometric function theory #Geometry and complex manifolds #Meromorphic and Entire Functions #math.CA #math.FA #math.PR #msc:60H99 #msc:65H99

paper · pdf · doi:10.48550/arxiv.1909.09411

9 pages

arxiv created 2019/10/16 · arxiv updated 2019/10/17

Abstract

The expected number of real zeros of an algebraic polynomial a₀+a₁x+a₂x²+a₃x³+....+a_n-1x^n-1 depends on the types of random coefficients, with large n. In this article, we show that when the random coefficients \a_i\_i=1^n-1 are assumed to be negatively dependent with var(a_i)=σ²ⁱ and correlation between any two coefficients for i≠ j, assumed to be ρ_ij=-ρ^|i-j|, where 0<ρ<(1)/(3), then the expected number of real zeros is asymptotically equal to (2)/(πσ)logn.

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