Event

Elliot Paquette - Ohio State University

Friday, February 8, 2019 14:00to15:00
Burnside Hall Room 708, 805 rue Sherbrooke Ouest, Montreal, QC, H3A 0B9, CA

 

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—dimensional beta—ensembles, a class of point processes that generalize random matrix eigenvalue distributions. We then outline directions of ongoing work to advance this notion of convergence.

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