Scaling limits of random normal matrix processes at singular boundary points
Probability
2019-10-10 v3 Mathematical Physics
Complex Variables
math.MP
Abstract
We give a method for taking microscopic limits of normal matrix ensembles. We apply this method to study the behaviour near certain types of singular points on the boundary of the droplet. Our investigation includes ensembles without restrictions near the boundary, as well as hard edge ensembles, where the eigenvalues are confined to the droplet. We establish in both cases existence of new types of determinantal point fields, which differ from those which can appear at a regular boundary point, or in the bulk.
Cite
@article{arxiv.1510.08723,
title = {Scaling limits of random normal matrix processes at singular boundary points},
author = {Yacin Ameur and Nam-Gyu Kang and Nikolai Makarov and Aron Wennman},
journal= {arXiv preprint arXiv:1510.08723},
year = {2019}
}
Comments
This (final) version contains some improvements with respect to presentation, correction of typos, and so on