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• W3103670695 abstract "Consider the zero set of the random power series f(z)=sum a_n z^n with i.i.d. complex Gaussian coefficients a_n. We show that these zeros form a determinantal process: more precisely, their joint intensity can be written as a minor of the Bergman kernel. We show that the number of zeros of f in a disk of radius r about the origin has the same distribution as the sum of independent {0,1}-valued random variables X_k, where P(X_k=1)=r^{2k}. Moreover, the set of absolute values of the zeros of f has the same distribution as the set {U_k^{1/2k}} where the U_k are i.i.d. random variables uniform in [0,1]. The repulsion between zeros can be studied via a dynamic version where the coefficients perform Brownian motion; we show that this dynamics is conformally invariant." @default.
• W3103670695 created "2020-11-23" @default.
• W3103670695 creator A5020836845 @default.
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• W3103670695 date "2005-01-01" @default.
• W3103670695 modified "2023-10-16" @default.
• W3103670695 title "Zeros of the i.i.d. Gaussian power series: a conformally invariant determinantal process" @default.
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• W3103670695 doi "https://doi.org/10.1007/bf02392515" @default.
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