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In the recent years, characteristic polynomial of random matrices have been considered with a growing interest as they allow to go beyond the classical results on the convergence of the spectral measure. Moreover, some random analytic functions which appear as limits of characteristic polynomials are of independent interest and are related to random fields. The goal of this talk is to explore these relations through a selection of random matrix models where two ubiquitous universal limits arise, namely the Gaussian and Poisson multiplicative chaos.