Limits of determinantal processes near a tacnode
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Author(s)
Duits, Maurice
Borodin, Alexei
Date Issued
February 2011
Journal
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
Publisher
Institute of Mathematical Statistics
Citation
Borodin, Alexei, and Maurice Duits. “Limits of Determinantal Processes near a Tacnode.” Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, vol. 47, no. 1, Feb. 2011, pp. 243–58.
Version
Original manuscript
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 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. The main result of the paper is a derivation of the local correlation kernel around the tacnode in the transition regime ε ↓ 0. We also prove that the local process interpolates between the Pearcey process and the GUE minor process.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1214/10-AIHP373
