• Corpus ID: 226237404

# Secular Coefficients and the Holomorphic Multiplicative Chaos

@article{Najnudel2020SecularCA,
title={Secular Coefficients and the Holomorphic Multiplicative Chaos},
author={Joseph Najnudel and Elliot Paquette and Nicholas J. Simm},
journal={arXiv: Probability},
year={2020}
}
• Published 3 November 2020
• Mathematics, Physics
• arXiv: Probability
We study the secular coefficients of $N \times N$ random unitary matrices $U_{N}$ drawn from the Circular $\beta$-Ensemble, which are defined as the coefficients of $\{z^n\}$ in the characteristic polynomial $\det(1-zU_{N}^{*})$. When $\beta > 4$ we obtain a new class of limiting distributions that arise when both $n$ and $N$ tend to infinity simultaneously. We solve an open problem of Diaconis and Gamburd by showing that for $\beta=2$, the middle coefficient tends to zero as $N \to \infty$. We…
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