Limits of determinantal processes near a tacnode

Abstract

We study a Markov process on a system of interlacing particles. At large times the particles fill a domain that depends on a parameter $\eps> 0$. The domain has two cusps, one pointing up and one pointing down. In the limit $\epsilon \downarrow 0$ 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 $\epsilon \downarrow 0$. We also prove that the local process interpolates between the Pearcey process and the GUE minor process.

16 pages, 9 figures

References in corpus (2)

• The Pearcey Process
• Asymptotics of Plancherel-type random partitions