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arXiv · 1808.02967

Central Limit Theorem for the volume of the zero set of Kostlan-Shub-Smale random polynomial systems

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

We state the Central Limit Theorem, as the degree goes to infinity, for the normalized volume of the zero set of a rectangular Kostlan-Shub-Smale random polynomial system. This paper is a continuation of {\it Central Limit Theorem for the number of real roots of Kostlan Shub Smale random polynomial systems} by the same authors in which the square case was considered. Our main tools are the Kac-Rice formula for the second moment of the volume of the zero set and an expansion of this random variable into the It\^o-Wiener Chaos.

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Jean-Marc Azaïs, Diego Armentano, Federico Dalmao, José R. León. 2018-08-08. Central Limit Theorem for the volume of the zero set of Kostlan-Shub-Smale random polynomial systems. https://arxiv.org/abs/1808.02967

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