English

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