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2014 Hole probabilities of $\mathrm{SU}(m+1)$ Gaussian random polynomials
Junyan Zhu
Anal. PDE 7(8): 1923-1967 (2014). DOI: 10.2140/apde.2014.7.1923

Abstract

In this paper, we study hole probabilities P0,m(r,N) of SU(m+1) Gaussian random polynomials of degree N over a polydisc (D(0,r))m. When r1, we find asymptotic formulas and the decay rate of logP0,m(r,N). In dimension one, we also consider hole probabilities over some general open sets and compute asymptotic formulas for the generalized hole probabilities Pk,1(r,N) over a disc D(0,r).

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Junyan Zhu. "Hole probabilities of $\mathrm{SU}(m+1)$ Gaussian random polynomials." Anal. PDE 7 (8) 1923 - 1967, 2014. https://doi.org/10.2140/apde.2014.7.1923

Information

Received: 2 April 2014; Revised: 13 August 2014; Accepted: 23 September 2014; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1311.32007
MathSciNet: MR3318744
Digital Object Identifier: 10.2140/apde.2014.7.1923

Subjects:
Primary: 32A60 , 60D05

Keywords: asymptotic , hole probability , SU(m+1) polynomial

Rights: Copyright © 2014 Mathematical Sciences Publishers

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Vol.7 • No. 8 • 2014
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