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Your search keyword '"Weak convergence"' showing total 1 results
Start Over Descriptor "Weak convergence" Topic analytic functions Publication Year Range Last 10 years Publication Type Academic Journals Journal communications in contemporary mathematics

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1 results on '"Weak convergence"'

1. Expected number of real zeroes of random Taylor series.

Author

Flasche, Hendrik and Kabluchko, Zakhar

Subjects
*REAL numbers, *RANDOM variables, *LIMIT theorems, *ANALYTIC functions, *TAYLOR'S series
Abstract

Let ξ 0 , ξ 1 , ... be i.i.d. random variables with zero mean and unit variance. Consider a random Taylor series of the form f (z) = ∑ k = 0 ∞ ξ k c k z k , where c 0 , c 1 , ... is a real sequence such that c n 2 is regularly varying with index γ − 1 , where γ > 0. We prove that 𝔼 N [ 0 , 1 − 𝜖 ] ∼ γ 2 π | log 𝜖 | as 𝜀 ↓ 0 , where N [ 0 , r ] denotes the number of real zeroes of f in the interval [ 0 , r ]. [ABSTRACT FROM AUTHOR]

Published
2020
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