Fluctuations for zeros of Gaussian Taylor series
| Autor: | Avner Kiro, Alon Nishry |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Mathematics - Complex Variables
Mathematics::Complex Variables General Mathematics Gaussian Probability (math.PR) 010102 general mathematics Variance (accounting) Covariance Taylor coefficients 01 natural sciences 010104 statistics & probability symbols.namesake FOS: Mathematics Taylor series symbols Applied mathematics Complex Variables (math.CV) 0101 mathematics Mathematics - Probability 30B20 (Primary) 30C15 (Secondary) Mathematics Analytic function |
| Zdroj: | Journal of the London Mathematical Society. 104:1172-1203 |
| ISSN: | 1469-7750 0024-6107 |
| Popis: | We study fluctuations in the number of zeros of random analytic functions given by a Taylor series whose coefficients are independent complex Gaussians. When the functions are entire, we find sharp bounds for the asymptotic growth rate of the variance of the number of zeros in large disks centered at the origin. To obtain a result that holds under no assumptions on the variance of the Taylor coefficients we employ the Wiman-Valiron theory. We demonstrate the sharpness of our bounds by studying well-behaved covariance kernels, which we call admissible (after Hayman). 37 pages |
| Databáze: | OpenAIRE |
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