A Riemann-Hilbert approach to the lower tail of the KPZ equation
arXiv:1910.02493
Abstract
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. We show that logarithmic derivatives of the Fredholm determinants can be expressed in terms of a 2x2 Riemann-Hilbert problem, and we 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, refining recent results by Corwin and Ghosal.
37 pages, 1 figure
References in corpus (4)
- Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
- Asymptotics in ASEP with Step Initial Condition
- Non-interacting fermions at finite temperature in a -dimensional trap: universal correlations
- Moments Match between the KPZ Equation and the Airy Point Process