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We give a method for taking microscopic limits of normal matrix ensembles. Weapply this method to study the behaviour near certain types of singular pointson the boundary of the droplet. Our investigation includes ensembles withoutrestrictions near the boundary, as well as hard edge ensembles, where theeigenvalues are confined to the droplet. We establish in both cases existenceof new types of determinantal point fields, which differ from those which canappear at a regular boundary point, or in the bulk.

Scaling limits of random normal matrix processes at singular boundary points