The airy and sine kernels define some determinantal point processes considered universal since they describe limiting behaviors in many random models such as random matrices, random partitions and fermionic systems at zero temperature. In these last models, when they are considered at non-zero temperature, some ''finite temperature'' deformations of the Airy and sine kernels appear.
In this talk we are going to compare the analytical properties of some spacing distributions in the corresponding determinantal point processes. In particular we will see that they still satisfy some Tracy-Widom formula, generalizing the well-known ones of the classical cases, and they are related to certain solutions of integrable partial differential equations.
