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Scaling limits of random normal matrix processes at singular boundary points

Ameur, Yacin and Kang, Nam-Gyu and Makarov, Nikolai and Wennman, Aron (2020) Scaling limits of random normal matrix processes at singular boundary points. Journal of Functional Analysis, 278 (3). Art. No. 108340. ISSN 0022-1236. https://resolver.caltech.edu/CaltechAUTHORS:20191011-112435530

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.jfa.2019.108340DOIArticle
https://arxiv.org/abs/1510.08723arXivDiscussion Paper
Additional Information:© 2019 Elsevier Inc. Received 13 January 2019, Accepted 20 September 2019, Available online 11 October 2019. Nam-Gyu Kang was supported by Samsung Science and Technology Foundation (SSTF-BA1401-01). Nikolai Makarov was supported by NSF grant no. 1500821. Aron Wennman was supported by the Knut and Alice Wallenberg (KAW) Foundation, and also by Vetenskapsrådet (VR), grant no. 2016-04912.
Funders:
Funding AgencyGrant Number
Samsung Science and Technology FoundationSSTF-BA1401-01
NSFDMS-1500821
Knut and Alice Wallenberg FoundationUNSPECIFIED
Vetenskapsrådet2016-04912
Subject Keywords:Random normal matrix; Singular boundary point; Scaling limit; Hard edge
Issue or Number:3
Classification Code:2010 Mathematics Subject Classification: Primary: 60B20. Secondary: 60G55; 30C40; 30D15; 35R09
Record Number:CaltechAUTHORS:20191011-112435530
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20191011-112435530
Official Citation:Yacin Ameur, Nam-Gyu Kang, Nikolai Makarov, Aron Wennman, Scaling limits of random normal matrix processes at singular boundary points, Journal of Functional Analysis, Volume 278, Issue 3, 2020, 108340, ISSN 0022-1236, https://doi.org/10.1016/j.jfa.2019.108340. (http://www.sciencedirect.com/science/article/pii/S0022123619303349)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99239
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:11 Oct 2019 18:33
Last Modified:15 Nov 2019 17:14

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