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- On the asymptotic variance of the number of real roots of random polynomial systems doi link

Auteur(s): Armentano D., Azaïs Jean-Marc, Dalmao F., Léon J.

(Article) Publié: Proceedings Of The American Mathematical Society, vol. 146 p.5437-5449 (2018)
Texte intégral en Openaccess : openaccess


Ref HAL: hal-01980703_v1
DOI: 10.1090/proc/14215
WoS: 000447836000039
Exporter : BibTex | endNote
4 Citations
Résumé:

We obtain the asymptotic variance, as the degree goes to infinity, of the normalized number of real roots of a square Kostlan-Shub-Smale random polynomial system of any size. Our main tools are the Kac-Rice formula for the second factorial moment of the number of roots and a Hermite expansion of this random variable.