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.
منابع مشابه
Strong Law of Large Numbers and Functional Central Limit Theorem
20.1. Additional technical results on weak convergence Given two metric spaces S1, S2 and a measurable function f : S1 → S2, suppose S1 is equipped with some probability measure P. This induces a probability measure on S2 which is denoted by Pf−1 and is defined by Pf−1(A) = P(f−1(A) for every measurable set A ⊂ S2. Then for any random variable X : S2 → R, its expectation EPf −1 [X] is equal to ...
متن کاملA Note on the Strong Law of Large Numbers
Petrov (1996) proved the connection between general moment conditions and the applicability of the strong law of large numbers to a sequence of pairwise independent and identically distributed random variables. This note examines this connection to a sequence of pairwise negative quadrant dependent (NQD) and identically distributed random variables. As a consequence of the main theorem ...
متن کاملStrong Law of Large Numbers with Concave Moments
It is observed that a wellnigh trivial application of the ergodic theorem from [3] yields a strong LLN for arbitrary concave moments. Not for publication: we found that Aaronson–Weiss essentially proved Theorem 1, see J. Aaronson, An introduction to infinite ergodic theory (AMS Math. Surv. Mon. 50, 1997), pages 65–66.
متن کاملStrong Law of Large Numbers and Central Limit Theorems for functionals of inhomogeneous Semi-Markov processes
Abstract: Limit theorems for functionals of classical (homogeneous) Markov renewal and semi-Markov processes have been known for a long time, since the pioneering work of R. Pyke and R. Schaufele (1964). Since then, these processes, as well as their time-inhomogeneous generalizations, have found many applications, for example in finance and insurance. Unfortunately, no limit theorems have been ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales Henri Lebesgue
سال: 2021
ISSN: ['2644-9463']
DOI: https://doi.org/10.5802/ahl.113