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We consider and compare two paradigmatic cases, namely: 1) the Complex Ginibre Ensemble conditioned on the existence of an outlier, and 2) the outlier induced by a rank-one Hermitian perturbation of a Complex Ginibre matrix. In both cases, we prove almost sure convergence towards a specific constant that only depends on the radius of the outlier and its status - either conditioned or induced.
These results can be generalized to other complex integrable ensembles with the same techniques, and complement our understanding of eigenvalue stability in non-Hermitian ensembles.
From: Lilou Thomas [view email]
[v1]
Mon, 15 Jun 2026 11:58:21 UTC (1,891 KB)
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