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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 β\beta 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}
}