Central Limit Theorem for the volume of the zero set of Kostlan-Shub-Smale random polynomial systems
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.
| 2021 | |
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Kostlan–Shub–Smale random polynomial systems Co-area formula Kac-Rice formula Central limit theorem |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/38119 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| Sumario: | Publicado también como: American Journal of Mathematics, 2021, 143(4): 1011-1042. DOI: 10.1353/ajm.2021.0026 |
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