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    Zeros of Random Reinhardt Polynomials

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    KARAMI-DISSERTATION-2014.pdf (447.2Kb)
    Date
    2014-07-01
    Author
    Karami, Arash
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    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.
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    http://jhir.library.jhu.edu/handle/1774.2/37945
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