Limits of determinantal processes near a tacnode

Details Limits of determinantal processes near a tacnode Limits of determinantal processes near a tacnode

2009-11-10

arxiv.org/abs/0911.1980v1

Mathematics

Probability

16 pages, 9 figures

Scientific paper

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 $\varepsilon\downarrow 0$ 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 $\varepsilon \downarrow 0$. We also prove that the local process interpolates between the Pearcey process and the GUE minor process.

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