Scaling limits of random normal matrix processes at singular boundary points
(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.
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https://lup.lub.lu.se/record/5a6d8c96-09d0-4e51-8621-9906e2e188c7
- author
- Ameur, Yacin LU ; Kang, Nam Gyu ; Makarov, Nikolai and Wennman, Aron LU
- organization
- publishing date
- 2020
- 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
- 2022-04-18 19:01:45
@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}}, keywords = {{Hard edge; Random normal matrix; Scaling limit; Singular boundary point}}, 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}}, }