Scaling limits of random normal matrix processes at singular boundary points

Yacin Ameur; Nam-Gyu Kang; Nikolai Makarov; Aron Wennman

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arXiv · 1510.08723

Scaling limits of random normal matrix processes at singular boundary points

Yacin Ameur·Nam-Gyu Kang·Nikolai Makarov·Aron Wennman

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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.

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BibTeX RIS

Yacin Ameur, Nam-Gyu Kang, Nikolai Makarov, Aron Wennman. 2019-10-09. Scaling limits of random normal matrix processes at singular boundary points. https://arxiv.org/abs/1510.08723

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