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.
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.
Accepted:
Published online:
Federico Dalmao 1, 2
@article{CRMATH_2015__353_12_1141_0, author = {Federico Dalmao}, title = {Asymptotic variance and {CLT} for the number of zeros of {Kostlan} {Shub} {Smale} random polynomials}, journal = {Comptes Rendus. Math\'ematique}, pages = {1141--1145}, publisher = {Elsevier}, volume = {353}, number = {12}, year = {2015}, doi = {10.1016/j.crma.2015.09.016}, language = {en}, }
TY - JOUR AU - Federico Dalmao TI - Asymptotic variance and CLT for the number of zeros of Kostlan Shub Smale random polynomials JO - Comptes Rendus. Mathématique PY - 2015 SP - 1141 EP - 1145 VL - 353 IS - 12 PB - Elsevier DO - 10.1016/j.crma.2015.09.016 LA - en ID - CRMATH_2015__353_12_1141_0 ER -
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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