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Gaussian analytic functions in the unit ball

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We study some properties of hyperbolic Gaussian analytic functions of intensity $L$ in the unit ball of $\mathbb{C}^n$. First we deal with the asymptotics of fluctuations of linear statistics as $L \rightarrow \infty$. Then we estimate the probability of large deviations (with respect to the expected value) of such linear statistics and use this estimate to prove a hole theorem.

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Israel Journal of Mathematics, 2015, num. 209, p. 855-881

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Articles publicats en revistes (Matemàtiques i Informàtica)

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Teoremes de límit (Teoria de probabilitats)

# metadata.dc.title[].value
Gaussian analytic functions in the unit ball