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.
Publié le : 2011-02-15
Classification:
Determinantal point processes,
Random growth,
GUE minor process,
Pearcey process,
82C22,
60K35,
60G55
@article{1294170237,
author = {Borodin, Alexei and Duits, Maurice},
title = {Limits of determinantal processes near a tacnode},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {47},
number = {1},
year = {2011},
pages = { 243-258},
language = {en},
url = {http://dml.mathdoc.fr/item/1294170237}
}
Borodin, Alexei; Duits, Maurice. Limits of determinantal processes near a tacnode. Ann. Inst. H. Poincaré Probab. Statist., Tome 47 (2011) no. 1, pp. 243-258. http://gdmltest.u-ga.fr/item/1294170237/