Maximum of the characteristic polynomial of random Jacobi matrices
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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