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Abstract: The Circular Beta Ensemble corresponds to a random set of N points on the unit circle whose probability density is proportional to the product of the mutual distances between the points, to the power beta. If the eigenvalue distribution of a random matrix corresponds to the Circular Beta Ensemble, we can consider its characteristic polynomial. In a joint work (in preparation) with Chhaibi and Madaule presented in this talk, we obtain, up to a tight family of random variables, the order of magnitude of the maximal modulus of this characteristic polynomial.