Limits of determinantal point processes near a tacnode
In this talk I will discuss a Markov process on a system of interlacing particles or, equivalently, lozenge tilings of the half plane. At large times the particles fill a domain that depends on a parameter ε> 0. The domain has two cusps, one pointing up and one pointing down. In the limit ε ↓ 0, the cusps touch, thus forming a tacnode. I will discuss the limiting process near the tacnode using a double scaling limit. I will also show how the new local process interpolates between the Pearcey process and the GUE minor process. This is joint work with Alexei Borodin (MIT).