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Expected number of real zeroes of random Taylor series.
- Source :
-
Communications in Contemporary Mathematics . Nov2020, Vol. 22 Issue 7, pN.PAG-N.PAG. 38p. - Publication Year :
- 2020
-
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]
- Subjects :
- *REAL numbers
*RANDOM variables
*LIMIT theorems
*ANALYTIC functions
*TAYLOR'S series
Subjects
Details
- Language :
- English
- ISSN :
- 02191997
- Volume :
- 22
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Communications in Contemporary Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 145106911
- Full Text :
- https://doi.org/10.1142/S0219199719500597