On the asymptotic variance of the number of real roots of random polynomial systems

Abstract : 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.
Document type :
Journal articles
Complete list of metadatas

Cited literature [19 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01980703
Contributor : Jean-Marc Azaïs <>
Submitted on : Wednesday, January 30, 2019 - 4:49:48 PM
Last modification on : Wednesday, May 29, 2019 - 9:46:18 AM

Identifiers

Citation

D. Armentano, J-M Azais, F. Dalmao, J. Leon. On the asymptotic variance of the number of real roots of random polynomial systems. Proceedings of the American Mathematical Society, American Mathematical Society, 2018, 146 (12), pp.5437-5449. ⟨10.1090/proc/14215⟩. ⟨hal-01980703⟩

Share

Metrics

Record views

74

Files downloads

65