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For an additive perturbation of the complex Ginibre ensemble under adeterministic matrix $X_0$, under certain assumption on $X_0$ we prove thatthere are only two types of local statistical patterns at the spectraledge--GinUE statistics and critical statistics, which corresponds to regular orquadratic vanishing spectral points. The latter, as a non-Hermitian analogue ofPearcey statistics in random matrix theory, characterizes a new point processon the complex plane and will be our major goal in this paper.

Critical edge statistics for deformed GinUEs