Maximum of the characteristic polynomial of random Jacobi matrices

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.

💡 Research Summary

The paper investigates the extreme value statistics of the logarithm of the absolute characteristic polynomial of random Jacobi matrices whose entries satisfy certain exponential integrability conditions. The authors consider a Jacobi matrix (J_n) with independent sequences ((a_k){k\ge1}) and ((b_k){k\ge1}) such that
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