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On the maximum of the characteristic polynomial of the Circular Beta Ensemble Najnudel, Joseph

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We present recent progess on the extremal values of (the logarithm of) the characteristic polynomial of a random unitary matrix whose spectrum is distributed according to the Circular Beta Ensemble. Using different techniques, it constitutes a follow-up to the work by Arguin, Belius, Bourgade on the one hand, and Paquette, Zeitouni on the other hand. They recently treated the CUE case, which corresponds to beta equal to 2

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