BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Benoît Kloeckner (Université Paris-Est - Créteil Val-de-Marne) DTSTART:20211012T133000Z DTEND:20211012T143000Z DTSTAMP:20260423T052335Z UID:Geometry/33 DESCRIPTION:Title: Effective high-temperature estimates ensuring a spectral gap\nby Ben oît Kloeckner (Université Paris-Est - Créteil Val-de-Marne) as part of Pangolin seminar\n\n\nAbstract\nThe main goal of the talk shall be to expl ain a few ideas from two classical theories : the thermodynamical formalis m\, and the perturbation of linear operators.\nThe "thermodynamical formal ism" is a framework to describe particular invariant measures of dynamical systems\, called "equilibrium states"\, parametrized by functions on the phase space\, called "potentials". This formalism is based on the "transfe r operator"\; when this operator has a spectral gap\, the equilibrium stat e exists\, is unique\, and has very good statistical properties (exponenti al mixing\, Central Limit Theorem\, etc.)\nIf one perturbs slightly the po tential\, the corresponding transfer operator is also perturbed.\nThe clas sical theory of perturbation of operators ensures that the spectral gap pr operty is an open condition and that under bounded pertubration\, the eige ndata of an operator depends analytically on the perturbation. It turns ou t that using the Implicit Function Theorem\, this theory can be made effec tive with explicit bounds on the size of a neighborhood where the spectral gap persists.\nUsing this effective perturbation theory\, we show complet ely explicit bound on the potential ensuring the spectral gap property for transfert operators of classical families of dynamical systems.\n LOCATION:https://researchseminars.org/talk/Geometry/33/ END:VEVENT END:VCALENDAR