Título:
Central Limit Theorem for the volume of the zero set of Kostlan-Shub-Smale random polynomial systems
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Autor:
Azaïs, J.M.
Armentano, Diego
Dalmao Artigas, Federico
León, José Rafael
Armentano, Diego
Dalmao Artigas, Federico
León, José Rafael
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Tipo de documento:
Preprint
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Palabras clave:
Kostlan–Shub–Smale random polynomial systems
Co-area formula
Kac-Rice formula
Central limit theorem
Co-area formula
Kac-Rice formula
Central limit theorem
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Año de publicación:
2021
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Resumen:
We state the Central Limit Theorem, as the degree goes to infinity, for the normalized volume of the zero set of a rectangular Kostlan-Shub-Smale random polynomial system. This paper is a continuation of {\it Central Limit Theorem for the number of real roots of Kostlan Shub Smale random polynomial systems} by the same authors in which the square case was considered. Our main tools are the Kac-Rice formula for the second moment of the volume of the zero set and an expansion of this random variable into the Itô-Wiener Chaos.
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Publicado también como: American Journal of Mathematics, 2021, 143(4): 1011-1042. DOI: 10.1353/ajm.2021.0026
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arXiv
EN:
Mathematics (Probability), arXiv:1801.06331, Sep 2021, pp 1-17
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Citación:
Azaïs, J, Armentano, D, Dalmao Artigas, F [y otro autor] "Central Limit Theorem for the volume of the zero set of Kostlan-Shub-Smale random polynomial systems". [Preprint]. Publicado en: Mathematics (Probability). 2021 arXiv:1801.06331, Sep 2021, pp 1-17 .
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Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
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| Ficheros | Descripción | Tamaño | Formato | ||
|---|---|---|---|---|---|
| 1808.02967.pdf | — | 288.57 KB | Adobe PDF |