Maximum of the characteristic polynomial of random Jacobi matrices
Probability
2025-12-16 v1
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 Ensembles, this result partially confirms the Fydorov-Simm conjecture.
Keywords
Cite
@article{arxiv.2512.13289,
title = {Maximum of the characteristic polynomial of random Jacobi matrices},
author = {Fanny Augeri and Ofer Zeitouni},
journal= {arXiv preprint arXiv:2512.13289},
year = {2025}
}