Fluctuations for zeros of Gaussian entire functions

Avner Kiro
Weizmann Institute of Science, Tel Aviv University, Israel

Date(s) : 09/12/2019   iCal
10 h 00 min - 11 h 00 min

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).



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