The order of the decay of the hole probability for Gaussian random SU(m+1) polynomials

2007/04/20 by Scott Zrebiec, Zrebiec, Scott · 2 citations
Mathematics · #Advanced Algebra and Geometry #Geometry and complex manifolds #Random Matrices and Applications #math.CV #math.PR #msc:30B20 #msc:30C15 #msc:60G60 #msc:82B10

paper · pdf · doi:10.48550/arxiv.0704.2733

This paper generalizes one which was previously posted by the author

arxiv created 2007/04/20 · arxiv updated 2009/12/01

Abstract

We show that for Gaussian random SU(m+1) polynomials of a large degree N the probability that there are no zeros in the disk of radius r is less than e^-c_1,r N^m+1, and is also greater than e^-c_2,r N^m+1. Enroute to this result, we also derive a more general result: probability estimates for the event where the volume of the zero set of a random polynomial of high degree deviates significantly from its mean.

Cited by

• Topics in the Value Distribution of Random Analytic Functions
• Estimates on the Probability of Outliers for Real Random Bargmann-Fock functions

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