Hole Probabilities of SU(m+1) Gaussian Random Polynomials

[摘要] 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).

[发布机构] Johns Hopkins University

[效力级别] SU(m+1) polynomial

[关键词] hole probability;SU(m+1) polynomial;Mathematics