The aim of this talk is to describe the various integrable probability models and integrable systems related to the Airy kernel and some of its recent generalizations that I worked on during the last years. In particular, we will focus on the properties of Fredholm determinants of the so-called finite temperature Airy kernel and its higher order analogues (based on a joint work with T. Bothner and M. Cafasso) and on the properties of a finite rank deformation of the same (based on ongoing work with T. Claeys, G. Glesner and G. Ruzza).

IPhT