Maximum of the characteristic polynomial of random Jacobi matrices

Fanny Augeri; Ofer Zeitouni

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arXiv · 2512.13289

Maximum of the characteristic polynomial of random Jacobi matrices

Fanny Augeri·Ofer Zeitouni

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Abstract

We compute the second order asymptotics of the maximum of the absolute value of the log-characteristic polynomial of random Jacobi matrices whose coefficients satisfy some exponential integrability condition. In particular, by the triadiagonal representation of Dumitriu and Eldelman of Gaussian $\beta$ Ensembles, this result partially confirms the Fydorov-Simm conjecture.

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Fanny Augeri, Ofer Zeitouni. 2025-12-15. Maximum of the characteristic polynomial of random Jacobi matrices. https://arxiv.org/abs/2512.13289

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