Uniform tail asymptotics for Airy kernel determinant solutions to KdV and for the narrow wedge solution to KPZ
Mathematical Physics
2022-07-27 v3 Analysis of PDEs
math.MP
Probability
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.
Keywords
Cite
@article{arxiv.2111.14569,
title = {Uniform tail asymptotics for Airy kernel determinant solutions to KdV and for the narrow wedge solution to KPZ},
author = {Christophe Charlier and Tom Claeys and Giulio Ruzza},
journal= {arXiv preprint arXiv:2111.14569},
year = {2022}
}
Comments
43 pages, 3 figures V2: minor revision