The tacnode Riemann-Hilbert problem
Classical Analysis and ODEs
2015-01-20 v1 Complex Variables
Abstract
The tacnode Riemann-Hilbert problem is a 4 x 4 matrix valued RH problem that appears in the description of the local behavior of two touching groups of non-intersecting Brownian motions. The same RH problem was also found by Duits and Geudens to describe a new critical regime in the two-matrix model. Delvaux gave integral representations for some of the entries of the 4 x 4 matrix. We complement this work by presenting integral representations for all of the entries. As a consequence we give an explicit formula for the Duits-Geudens critical kernel.
Cite
@article{arxiv.1304.6227,
title = {The tacnode Riemann-Hilbert problem},
author = {Arno Kuijlaars},
journal= {arXiv preprint arXiv:1304.6227},
year = {2015}
}
Comments
29 pages, 5 figures