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Israel Journal of Mathematics
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Preprint . 2002
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Random complex zeroes, I. Asymptotic normality

Random complex zeroes. I: Asymptotic normality
descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Mar 2004Embargo end date: 01 Jan 2002 English Publisher:Springer Science and Business Media LLCJournal:Israel Journal of Mathematics, volume 144, pages 125-149 (issn: 0021-2172, Copyright policy )
Authors: Sodin, Mikhail; Tsirelson, Boris;

doi: 10.1007/bf02984409 , 10.48550/arxiv.math/0210090

arXiv: math/0210090

Random complex zeroes, I. Asymptotic normality

Abstract

We consider three models (elliptic, flat and hyperbolic) of Gaussian random analytic functions distinguished by invariance of their zeroes distribution. Asymptotic normality is proven for smooth functionals (linear statistics) of the set of zeroes.

26 pages. Version 2 (final): the end of the proof corrected (sections 3.2, 3.3); small insertions to Introduction and References

Related Organizations
Keywords

Mathematics - Complex Variables, Probability (math.PR), FOS: Physical sciences, 30B20, Mathematical Physics (math-ph), analytic functions, 30C15, 60G60, 82B10, Stochastic processes, randon polynomials, FOS: Mathematics, Complex Variables (math.CV), Gaussian random variables, Mathematical Physics, Mathematics - Probability, 30B20; 30C15, 60G60, 82B10

  • BIP!
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    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 74
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
74
Top 10%
Top 10%
Average
Green
bronze