Expected number of real roots for random linear combinations of orthogonal polynomials associated with radial weights

Turgay Bayraktar

doi:10.1007/s11118-017-9643-9

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arXiv · 1611.04695

Expected number of real roots for random linear combinations of orthogonal polynomials associated with radial weights

Turgay Bayraktar

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Abstract

In this note, we obtain asymptotic expected number of real zeros for random polynomials of the form $$f_n(z)=\sum_{j=0}^na^n_jc^n_jz^j$$ 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.

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BibTeX RIS

Turgay Bayraktar. 2017-05-22. Expected number of real roots for random linear combinations of orthogonal polynomials associated with radial weights. https://doi.org/10.1007/s11118-017-9643-9

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