Zeros of Random Reinhardt Polynomials
[摘要] For a strictly pseudoconvex Reinhardt domain Ω with smooth boundary in Cm+1and a positive smooth measure µ on the boundary of Ω , we consider the ensemblePN of polynomials of degree N with the Gaussian probability measure γN which isinduced by L2(∂Ω, dµ). Our aim is to compute the scaling limit distribution functionand scaling limit pair correlation function for zeros near a point z ∈ ∂Ω. First, weapply the stationary phase method to the Boutet de Monvel-Sj¨ostrand Theorem toget the asymptotic for the scaling limit partial Szeg¨o kernel around z ∈ ∂Ω. Thenby using the Kac-Rice formula, we compute the scaling limit distribution and paircorrelation functions.
[发布日期] [发布机构] Johns Hopkins University
[效力级别] Szeg¨o kernel [学科分类]
[关键词] Reinhardt domain;Szeg¨o kernel;Mathematics [时效性]
