BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Elliot Paquette (McGill University) DTSTART:20201211T143000Z DTEND:20201211T153000Z DTSTAMP:20260423T005735Z UID:MEGA/11 DESCRIPTION:Title: Th e edge scaling limit of the Gaussian beta-ensemble characteristic polynomi al\nby Elliot Paquette (McGill University) as part of Séminaire MEGA\ n\n\nAbstract\nThe Gaussian beta-ensemble (GbetaE) is a 1-parameter genera lization of the Gaussian orthogonal/unitary/symplectic ensembles which ret ains some integrable structure. Using this ensemble\, in Ramirez\, Rider a nd Virag constructed a limiting point process\, the Airy-beta point proces s\, which is the weak limit of the point process of eigenvalues in a neigh borhood of the spectral edge. They constructed a limiting Sturm—Liouvill e problem\, the stochastic Airy equation with Dirichlet boundary condition s\, and they proved convergence of a discrete operator with spectra given by GbetaE to this limit.\n\nJointly with Gaultier Lambert\, we give a cons truction of a new limiting object\, the stochastic Airy function (SAi)\; w e also show this is the limit of the characteristic polynomial of GbetaE i n a neighborhood of the edge. It is the solution of the stochastic Airy eq uation\, which is the usual Airy equation perturbed by a multiplicative wh ite noise\, with specified asymptotics at time=+infinity. Its zeros are gi ven by the Airy-beta point process\, and the mode of convergence we establ ish provides a new proof that Airy-beta is the limiting point process of e igenvalues of GbetaE. In this talk\, we survey what new information we hav e on the characteristic polynomial\; we show from where the stochastic Air y equation arises\; we show how SAi is constructed\; and we leave some una nswered questions.\n LOCATION:https://researchseminars.org/talk/MEGA/11/ END:VEVENT END:VCALENDAR