Advanced

Scaling limits of random normal matrix processes at singular boundary points

Ameur, Yacin LU ; Kang, Nam Gyu ; Makarov, Nikolai and Wennman, Aron LU (2020) In Journal of Functional Analysis 278(3).
Abstract

We introduce a method for taking microscopic limits of normal matrix ensembles and apply it 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.

Please use this url to cite or link to this publication:
author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Hard edge, Random normal matrix, Scaling limit, Singular boundary point
in
Journal of Functional Analysis
volume
278
issue
3
article number
108340
publisher
Elsevier
external identifiers
  • scopus:85074763586
ISSN
0022-1236
DOI
10.1016/j.jfa.2019.108340
language
English
LU publication?
yes
id
5a6d8c96-09d0-4e51-8621-9906e2e188c7
date added to LUP
2019-11-28 07:56:26
date last changed
2020-10-07 06:47:48
@article{5a6d8c96-09d0-4e51-8621-9906e2e188c7,
  abstract     = {<p>We introduce a method for taking microscopic limits of normal matrix ensembles and apply it 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.</p>},
  author       = {Ameur, Yacin and Kang, Nam Gyu and Makarov, Nikolai and Wennman, Aron},
  issn         = {0022-1236},
  language     = {eng},
  number       = {3},
  publisher    = {Elsevier},
  series       = {Journal of Functional Analysis},
  title        = {Scaling limits of random normal matrix processes at singular boundary points},
  url          = {http://dx.doi.org/10.1016/j.jfa.2019.108340},
  doi          = {10.1016/j.jfa.2019.108340},
  volume       = {278},
  year         = {2020},
}