University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > The lower tail of the KPZ equation via a Riemann-Hilbert approach

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

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact INI IT.

CATW02 - Complex analysis in mathematical physics and applications

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2021 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity