On the asymptotic variance of the number of real roots of random polynomial systems
Résumé
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.
Domaines
Probabilités [math.PR]
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