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Gaussian analytic functions in the unit ball

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Abstract

We study some properties of hyperbolic Gaussian analytic functions of intensity L in the unit ball of ℂn. First we deal with the asymptotics of fluctuations of linear statistics as L → ∞. 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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Authors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, Tel Aviv, 69978, Israel

    Jeremiah Buckley

  2. Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08071, Barcelona, Spain

    Xavier Massaneda & Bharti Pridhnani

Authors
  1. Jeremiah Buckley
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  2. Xavier Massaneda
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  3. Bharti Pridhnani
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Corresponding author

Correspondence to Jeremiah Buckley.

Additional information

Authors supported by the Generalitat de Catalunya (grant 2014 SGR 00289) and the Spanish Ministerio de Economía y Competividad (projects MTM2011-27932-C02-01).

The first author is also supported by the Raymond and Beverly Sackler Post-Doctoral Scholarship.

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Buckley, J., Massaneda, X. & Pridhnani, B. Gaussian analytic functions in the unit ball. Isr. J. Math. 209, 855–881 (2015). https://doi.org/10.1007/s11856-015-1239-8

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  • DOI: https://doi.org/10.1007/s11856-015-1239-8

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