Central Limit Theorem for the number of real roots of random orthogonal polynomials (2111.09015v1)

Published 17 Nov 2021 in math.PR and math.CA

Abstract: In this note we study the number of real roots of a wide class of random orthogonal polynomials with gaussian coefficients. Using the method of Wiener Chaos we show that the fluctuation in the bulk is asymptotically gaussian, even when the local correlations are not necessarily the same.

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