Comptes Rendus
no. 12
Probability theory
Asymptotic variance and CLT for the number of zeros of Kostlan Shub Smale random polynomials
[Variance asymptotique et TCL pour le nombre de zéros des polynômes aléatoires de Kostlan–Shub–Smale]

Présenté par : the Editorial Board

Federico Dalmao1, 2
1 Departamento de Matemática y Estadística del Litoral, Universidad de la República, CP 50000, Salto, Uruguay
2 Unité de Recherche en Mathématiques, Université du Luxembourg, campus Kirchberg, L-1359, Luxembourg
Comptes Rendus. Mathématique, Volume 353 (2015) no. 12, pp. 1141-1145.

Dans cette note, nous calculons un equivalent de la variance asymptotique du nombre de racines réelles des polynômes aléatoires de Kostlan–Shub–Smale et nous démontrons un théorème de la limite centrale pour ce même nombre quand le degré tend vers l'infini.

In this note, we find the asymptotic main term of the variance of the number of roots of Kostlan–Shub–Smale random polynomials and prove a central limit theorem for this number of roots as the degree goes to infinity.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.09.016
Federico Dalmao 1, 2

1 Departamento de Matemática y Estadística del Litoral, Universidad de la República, CP 50000, Salto, Uruguay
2 Unité de Recherche en Mathématiques, Université du Luxembourg, campus Kirchberg, L-1359, Luxembourg 
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     journal = {Comptes Rendus. Math\'ematique},
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Federico Dalmao. Asymptotic variance and CLT for the number of zeros of Kostlan Shub Smale random polynomials. Comptes Rendus. Mathématique, Volume 353 (2015) no. 12, pp. 1141-1145. doi : 10.1016/j.crma.2015.09.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.09.016/

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