Maximum of the characteristic polynomial of random Jacobi matrices

2025/12/15 by Fanny Augeri, Augeri, Fanny, Ofer Zeitouni +1
Mathematics · #FOS: Mathematics #Geometry and complex manifolds #Mathematical functions and polynomials #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2512.13289

openalex publication_date 2025/12/15 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/28

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 Ensembles, this result partially confirms the Fydorov-Simm conjecture.

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