The extremal landscape for the C$\beta$E ensemble
Probability
2024-10-24 v3
Abstract
We consider the extremes of the logarithm of the characteristic polynomial of matrices from the CE 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.
Keywords
Cite
@article{arxiv.2209.06743,
title = {The extremal landscape for the C$\beta$E ensemble},
author = {Elliot Paquette and Ofer Zeitouni},
journal= {arXiv preprint arXiv:2209.06743},
year = {2024}
}
Comments
Appendix B is an adaptation of estimates from arXiv:1607.00243 and uses their source file as template. V3 incorporates numerous comments of the referee and makes numerous corrections throughout the paper. To appear in Forum of Mathematics, Sigma