On the asymptotic variance of the number of real roots of random polynomial systems

arxiv: 1703.08163 · v3 · pith:LEER3US3new · submitted 2017-03-23 · 🧮 math.PR

On the asymptotic variance of the number of real roots of random polynomial systems

Diego Armentano , Jean-Marc Aza\"is , Federico Dalmao , Jos\'e R. Le\'on This is my paper

classification 🧮 math.PR

keywords numberrandomrootsasymptoticpolynomialrealvariancedegree

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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.

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On the asymptotic variance of the number of real roots of random polynomial systems

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