Hole Probabilities of SU(m+1) Gaussian Random Polynomials
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Date
2015-06-22
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Johns Hopkins University
Abstract
In this paper, we study hole probabilities P_{0,m}(r,N) of SU(m+1) Gaussian random polynomials of degree N over a polydisk (D(0,r))^m. When r>=1, we derive asymptotic formulas and decay rate of log P_{0,m}(r,N). In one dimensional case, we also consider hole probabilities over some general open sets and compute asymptotic formulas for the generalized hole probabilities P_{k,1}(r,N) over a disk D(0,r).
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Keywords
hole probability, SU(m+1) polynomial