Zeros of random Reinhardt polynomials
| Autor: | Arash Karami |
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| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Complex Variables and Elliptic Equations. 60:801-828 |
| ISSN: | 1747-6941 1747-6933 |
| DOI: | 10.1080/17476933.2014.976816 |
| Popis: | For a strictly pseudoconvex Reinhardt domain with smooth boundary in and a positive smooth measure on the boundary of , we consider the ensemble of polynomials of degree N with the Gaussian probability measure which is induced by . Our aim is to compute the scaling limit distribution function and scaling limit pair correlation function for zeros near a point . First, we apply the stationary phase method to the Boutet de Monvel–Sjostrand Theorem to get the asymptotic for the scaling limit partial Szego kernel around . Then by using the Kac–Rice formula, we compute the scaling limit distribution and pair correlation functions. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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