Vol. 7, No. 8, 2014

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Hole probabilities of $\mathrm{SU}(m+1)$ Gaussian random polynomials

Junyan Zhu

Vol. 7 (2014), No. 8, 1923–1967
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 r 1, 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).

Keywords
hole probability, asymptotic, SU(m+1) polynomial
Mathematical Subject Classification 2010
Primary: 32A60, 60D05
Milestones
Received: 2 April 2014
Revised: 13 August 2014
Accepted: 23 September 2014
Published: 5 February 2015
Authors
Junyan Zhu
Department of Mathematics
Johns Hopkins University
3400 N. Charles St.
Krieger 404
Baltimore, MD 21218
United States