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- W2230837103 abstract "We study hyperbolic Gaussian analytic functions in the unit polydisk of (mathbb {C}^n). Following the scheme previously used in the unit ball, we first study the asymptotics of fluctuations of linear statistics as the directional intensities (L_j), (j=1,dots ,n) tend to (infty ). Then, we estimate the probability of large deviations of such linear statistics and use the estimate to prove a hole theorem. Our proofs are inspired by the methods of M. Sodin and B. Tsirelson for the one-dimensional case, and B. Shiffman and S. Zelditch for the study of the analogous problem for compact Kahler manifolds." @default.
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- W2230837103 date "2017-03-14" @default.
- W2230837103 modified "2023-09-24" @default.
- W2230837103 title "Gaussian Analytic Functions in the Polydisk" @default.
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- W2230837103 doi "https://doi.org/10.1007/s00009-017-0892-z" @default.
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