Elliot Paquette - Ohio State University
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Title: The characteristic polynomial of random matrices and the Gaussian multiplicative chaos
Abstract: Conjecturally, the characteristic polynomials of many canonical classes of random matrices converge to a universal random measure, the Gaussian multiplicative chaos. This convergence captures the extreme value behavior of many interesting random matrix quantities, and there is a substantial body of work around it with interesting connections to the theory of branching processes and analytic number theory, among others. We survey the current state of the art of this convergence for one鈥攄imensional beta鈥攅nsembles, a class of point processes that generalize random matrix eigenvalue distributions. We then outline directions of ongoing work to advance this notion of convergence.