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Potential Analysis

, Volume 48, Issue 4, pp 459–471 | Cite as

Expected Number of Real Roots for Random Linear Combinations of Orthogonal Polynomials Associated with Radial Weights

  • Turgay Bayraktar
Article
  • 39 Downloads

Abstract

In this note, we obtain asymptotic expected number of real zeros for random polynomials of the form
$$f_{n}(z)=\sum\limits_{j=0}^{n}{a^{n}_{j}}{c^{n}_{j}}z^{j}$$
where \({a^{n}_{j}}\) are independent and identically distributed real random variables with bounded (2 + δ)th absolute moment and the deterministic numbers \({c^{n}_{j}}\) are normalizing constants for the monomials z j within a weighted L 2-space induced by a radial weight function satisfying suitable smoothness and growth conditions.

Keywords

Expected number of real zeros Random orthogonal polynomials 

Mathematics Subject Classification (2010)

30C15 60G99 

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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Faculty of Engineering and Natural SciencesSabancı UniversityİstanbulTurkey

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