Fredholm 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.

中文翻译：

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Kardar-Parisi-Zhang 方程下尾的 Riemann-Hilbert 方法

与 Airy 核变形相关的 Fredholm 行列式与具有窄楔形初始数据的 Kardar-Parisi-Zhang (KPZ) 方程的解密切相关，并且它们在正温自由费米子模型中也表现为最大粒子分布。