Uniform tail asymptotics for Airy kernel determinant solutions to KdV and for the narrow wedge solution to KPZ

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.

arXiv comment43 pages, 3 figures V2: minor revision

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• Universality for multiplicative statistics of Hermitian random matrices and the integro-differential Painlevé II equation
• Jánossy densities and Darboux transformations for the Stark and cylindrical KdV equations
• Integrable equations associated with the finite-temperature deformation of the discrete Bessel point process
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