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Published February 1, 2020 | public
Journal Article Open

Scaling limits of random normal matrix processes at singular boundary points


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.

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.

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August 22, 2023
August 22, 2023