On the asymptotic variance of the number of real roots of random polynomial systems 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 : 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. |