Zeros of Random Reinhardt Polynomials

Reinhardt domain;Szeg¨o kernel;Mathematics

Karami, ArashShiffman, Bernard ;

Johns Hopkins University

关键词: Reinhardt domain;    Szeg¨o kernel;    Mathematics;   

Others  :  https://jscholarship.library.jhu.edu/bitstream/handle/1774.2/37945/KARAMI-DISSERTATION-2014.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: JOHNS HOPKINS DSpace Repository

【 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.