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The lower tail of the KPZ equation via a Riemann-Hilbert approach

Presented by: 
Tom Claeys Université Catholique de Louvain
Tuesday 29th October 2019 - 14:30 to 15:30
INI Seminar Room 1
Fredholm determinants associated to deformations of the Airy kernel are closely connected to the solution to the Kardar-Parisi-Zhang (KPZ) equation with narrow wedge initial data, and they also appear as largest particle distribution in models of positive-temperature free fermions. I will explain how logarithmic derivatives of the Fredholm determinants can be expressed in terms of a $2\times 2$ Riemann-Hilbert problem, and how we can use this to derive asymptotics for the Fredholm determinants. As an application of our result, we derive precise lower tail asymptotics for the solution of the KPZ equation with narrow wedge initial data which refine recent results by Corwin and Ghosal.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons