Uniform tail asymptotics for Airy kernel determinant solutions to KdV and for the narrow wedge solution to KPZ
arXiv:2111.14569 · doi:10.1016/j.jfa.2022.109608
Abstract
We obtain uniform asymptotics for deformed Airy kernel determinants, which arise in models of finite temperature free fermions and which characterize the narrow wedge solution of the Kardar-Parisi-Zhang equation. The asymptotics for the determinants yield uniform initial data for an associated family of solutions to the Korteweg-de Vries equation, and uniform lower tail asymptotics for the narrow wedge solution of the Kardar-Parisi-Zhang equation.
43 pages, 3 figures V2: minor revision