%0 Journal Article
%T On the asymptotic variance of the number of real roots of random polynomial systems
%+ Institut de Mathématiques de Toulouse UMR5219 (IMT)
%+ Laboratoire Charles Coulomb (L2C)
%A Armentano, D.
%A Azaïs, Jean-Marc
%A Dalmao, F.
%A Leon, J.
%< avec comité de lecture
%@ 0002-9939
%J Proceedings of the American Mathematical Society
%I American Mathematical Society
%V 146
%N 12
%P 5437-5449
%8 2018-12-01
%D 2018
%R 10.1090/proc/14215
%Z Mathematics [math]/Probability [math.PR]Journal articles
%X 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.
%G English
%2 https://hal.science/hal-01980703/document
%2 https://hal.science/hal-01980703/file/KSS-arxiv-3.pdf
%L hal-01980703
%U https://hal.science/hal-01980703
%~ UNIV-TLSE2
%~ UNIV-TLSE3
%~ CNRS
%~ INSA-TOULOUSE
%~ L2C
%~ IMT
%~ UT1-CAPITOLE
%~ MIPS
%~ UNIV-MONTPELLIER
%~ INSA-GROUPE
%~ TEST-HALCNRS
%~ UNIV-UT3
%~ UT3-INP
%~ UT3-TOULOUSEINP
%~ UM-2015-2021