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

Diego Armentano; Jean-Marc Azaïs; Federico Dalmao; José R. León

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arXiv · 1703.08163

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

Diego Armentano·Jean-Marc Azaïs·Federico Dalmao·José R. León

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Abstract

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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Diego Armentano, Jean-Marc Azaïs, Federico Dalmao, José R. León. 2017-03-23. On the asymptotic variance of the number of real roots of random polynomial systems. https://arxiv.org/abs/1703.08163

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