Roots of Kostlan polynomials: moments, strong Law of Large Numbers and Central Limit Theorem

نویسندگان

چکیده

We study the number of real roots a Kostlan random polynomial degree d in one variable. More generally, we consider counting measure set such polynomials. compute large asymptotics central moments these variables. As consequence, obtain strong Law Large Numbers and Central Limit Theorem. In particular, almost surely equidistribute as diverges. Moreover, fluctuations their converge distribution to Standard Gaussian White Noise. our results hold for zeros section complex Fubini–Study model.

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ژورنال

عنوان ژورنال: Annales Henri Lebesgue

سال: 2021

ISSN: ['2644-9463']

DOI: https://doi.org/10.5802/ahl.113