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

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 polydisc $(D(0,r){)}^m$. When $r\ge 1$, we find asymptotic formulas and 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 $D(0,r)$.

35 pages

References in corpus (2)

• Zeros of the i.i.d. Gaussian power series: a conformally invariant determinantal process
• Asymptotics of The Hole Probability for Zeros of Random Entire Functions

Cited by in corpus (1)

• Holomorphic Line Bundles over a Tower of Coverings