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Comptes Rendus Mathématique
Volume 353, n° 12
pages 1141-1145 (décembre 2015)
Doi : 10.1016/j.crma.2015.09.016
Received : 28 April 2015 ;  accepted : 17 September 2015
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
 

Federico Dalmao a, b
a Departamento de Matemática y Estadística del Litoral, Universidad de la República, CP 50000, Salto, Uruguay 
b Unité de Recherche en Mathématiques, Université du Luxembourg, campus Kirchberg, L-1359, Luxembourg 

Abstract

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.

The full text of this article is available in PDF format.
Résumé

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.

The full text of this article is available in PDF format.


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