Extreme value statistics for the roots of a complex Kac polynomial

Yacine Barhoumi-Andréani

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arXiv · 1706.07516

Extreme value statistics for the roots of a complex Kac polynomial

Yacine Barhoumi-Andréani

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Abstract

We investigate the fluctuations and large deviations of the root of largest modulus in a model of random polynomial with independent complex Gaussian coefficients (Kac polynomials). The fluctuations were recently computed by R. Butez (arxiv 1704.02761) and involve a Fredholm determinant. The precise large deviations show a particular function defined by a series of mutiple integrals in the same vein.

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Yacine Barhoumi-Andréani. 2017-06-22. Extreme value statistics for the roots of a complex Kac polynomial. https://arxiv.org/abs/1706.07516

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