Hole probabilities of SU(m + 1) Gaussian random polynomials

In this paper, we study hole probabilities $P_{0, m} (r, N)$ of $SU (m + 1)$ Gaussian random polynomials of degree $N$ over a polydisc ${(D (0, r))}^{m}$ . When $r \geq 1$ , we find asymptotic formulas and the decay rate of $log P_{0, m} (r, N)$ . In dimension one, we also consider hole probabilities over some general open sets and compute asymptotic formulas for the generalized hole probabilities $P_{k, 1} (r, N)$ 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

Vol. 7, No. 8, 2014

Junyan Zhu

Abstract

Keywords

Mathematical Subject Classification 2010

Milestones

Authors