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SUMMARY:The lower tail of the KPZ equation via a Riemann-Hilbert approach 
 - Tom Claeys (Université Catholique de Louvain )
DTSTART:20191029T143000Z
DTEND:20191029T153000Z
UID:TALK133300@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Fredholm determinants associated to deformations of the Airy k
 ernel are closely connected to the solution to the Kardar-Parisi-Zhang (KP
 Z) equation with narrow wedge initial data\, and they also appear as large
 st particle distribution in models of positive-temperature free fermions. 
 I will explain how logarithmic derivatives of the Fredholm determinants ca
 n be expressed in terms of a $2\\times 2$ Riemann-Hilbert problem\, and ho
 w we can use this to derive asymptotics for the Fredholm determinants. As 
 an application of our result\, we derive precise lower tail asymptotics fo
 r the solution of the KPZ equation with narrow wedge initial data which re
 fine recent results by Corwin and Ghosal.
LOCATION:Seminar Room 1\, Newton Institute
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