Limits of determinantal processes near a tacnode

We study a Markov process on a system of interlacing particles. At large times the particles fill a domain that depends on a parameter epsilon > 0. The domain has two cusps, one pointing up and one pointing down. In the limit epsilon down arrow 0 the cusps touch, thus forming a tacnode. The main result of the paper is a derivation of the local correlation kernel around the tacnode in the transition regime epsilon down arrow 0. We also prove that the local process interpolates between the Pearcey process and the GUE minor process.