BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Tom Claeys (Université Catholique de Louvain) DTSTART:20200928T160000Z DTEND:20200928T170000Z DTSTAMP:20260423T024723Z UID:QM3/18 DESCRIPTION:Title: Def ormed Airy kernel determinants: from KPZ tails to initial data for KdV \nby Tom Claeys (Université Catholique de Louvain) as part of Quantum Mat ter meets Maths (IST\, Lisbon)\n\n\nAbstract\nFredholm determinants associ ated to deformations of the Airy kernel are closely connected to the solut ion to the Kardar-Parisi-Zhang (KPZ) equation with narrow wedge initial da ta\, and they also appear as largest particle distribution in models of po sitive-temperature free fermions. I will explain how logarithmic derivativ es of the Fredholm determinants can be expressed in terms of a $2\\times 2 $ Riemann-Hilbert problem.\nThis Riemann-Hilbert representation can be use d to derive precise lower tail asymptotics for the solution of the KPZ equ ation with narrow wedge initial data\, refining recent results by Corwin a nd Ghosal\, and it reveals a remarkable connection with a family of unboun ded solutions to the Korteweg-de Vries (KdV) equation and with an integro- differential version of the Painlevé II equation.\n LOCATION:https://researchseminars.org/talk/QM3/18/ END:VEVENT END:VCALENDAR