Expected number of real roots for random linear combinations of orthogonal polynomials associated with radial weights
Bayraktar, Turgay (2018) Expected number of real roots for random linear combinations of orthogonal polynomials associated with radial weights. Potential Analysis, 48 (4). pp. 459-471. ISSN 0926-2601 (Print) 1572-929X (Online)
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Official URL: http://dx.doi.org/10.1007/s11118-017-9643-9
In this note, we obtain asymptotic expected number of real zeros for random polynomials of the form fn(z) = Sigma(n)(j=0) 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 aradial weight function satisfying suitable smoothness and growth conditions.
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