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

Abstract

In this note, we obtain asymptotic expected number of real zeros for random polynomials of the form $$f_n(z)=\sum _{j=0}^n{a}_j^n{c}_j^n{z}^j$$ where $a_j^n$ are independent and identically distributed real random variables with bounded $(2+\delta )$th absolute moment and the deterministic numbers $c_j^n$ 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.

Change in title, minor revisions

References in corpus (3)

• Universality for zeros of random analytic functions
• Asymptotic normality of linear statistics of zeros of random polynomials
• Expected number of real zeros for random linear combinations of orthogonal polynomials

Cited by in corpus (4)

• Variance of the volume of random real algebraic submanifolds II
• On global universality for zeros of random polynomials
• A survey on zeros of random holomorphic sections
• An Exponential Rarefaction Result for Sub-Gaussian Real Algebraic Maximal Curves