article · 2012
Abstract. Consider a Gaussian Entire Function
F. Nazarov, M. Sodin, A. Volberg
Cited by 0Abstract and details only
Abstract
∞ ∑ z f(z) = k k! k=0 where ζ0, ζ1,... are Gaussian i.i.d. complex random variables. The zero set of this function is distribution invariant with respect to the isometries of the complex plane. Let n(R) be the number of zeroes of f in the disk of radius R. It is easy to see that En(R) = R 2, and it is known that the variance of n(R) grows linearly with R (Forrester and Honner). We prove that, for every α> 1/2, the tail probability P { |n(R)−R 2 |> R α} behaves as exp [ −R ϕ(α)] with some explicit piecewise linear function ϕ(α). For some special values of the parameter α, this law was found earlier by Sodin and Tsirelson, and by Krishnapur. In the context of charge fluctuations of a one-component Coulomb system of particles of one sign embedded into a uniform background of another sign, a similar law was discovered some time ago by Jancovici, Lebowitz and Magnificat. ζk
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Nazarov, F., Sodin, M., & Volberg, A. (2012). Abstract. Consider a Gaussian Entire Function.
Nazarov, F., et al. “Abstract. Consider a Gaussian Entire Function.” 2012.
Nazarov, F., M. Sodin, and A. Volberg. 2012. “Abstract. Consider a Gaussian Entire Function.”
Nazarov, F., Sodin, M. and Volberg, A. (2012) ‘Abstract. Consider a Gaussian Entire Function’.
@article{nazarov2012abstract,
title = {{Abstract. Consider a Gaussian Entire Function}},
author = {Nazarov, F. and Sodin, M. and Volberg, A.},
year = {2012}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.