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arXiv · 2209.06743

The extremal landscape for the C$\beta$E ensemble

Elliot Paquette·Ofer Zeitouni
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Abstract

We consider the extremes of the logarithm of the characteristic polynomial of matrices from the C$\beta$E ensemble. We prove convergence in distribution of the centered maxima (of the real and imaginary parts) towards the sum of a Gumbel variable and another independent variable, which we characterize as the total mass of a "derivative martingale". We also provide a description of the landscape near extrema points.

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Elliot Paquette, Ofer Zeitouni. 2022-09-14. The extremal landscape for the C$\beta$E ensemble. https://arxiv.org/abs/2209.06743

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