Zeros of Random Reinhardt Polynomials
Embargo until
Date
2014-07-01
Authors
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Journal ISSN
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Publisher
Johns Hopkins University
Abstract
For a strictly pseudoconvex Reinhardt domain Ω with smooth boundary in C
m+1
and a positive smooth measure µ on the boundary of Ω , we consider the ensemble
PN of polynomials of degree N with the Gaussian probability measure γN which is
induced by L
2
(∂Ω, dµ). Our aim is to compute the scaling limit distribution function
and scaling limit pair correlation function for zeros near a point z ∈ ∂Ω. First, we
apply the stationary phase method to the Boutet de Monvel-Sj¨ostrand Theorem to
get the asymptotic for the scaling limit partial Szeg¨o kernel around z ∈ ∂Ω. Then
by using the Kac-Rice formula, we compute the scaling limit distribution and pair
correlation functions.
Description
Keywords
Reinhardt domain, Szeg¨o kernel