Abstract
AbstractFredholm 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 distributions in models of positive‐temperature free fermions.We show that logarithmic derivatives of the Fredholm determinants can be expressed in terms of a 2 × 2 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. © 2021 Wiley Periodicals LLC.
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