Abstract
We study the limiting distribution of the eigenvalues of the Ginibre ensemble conditioned on the event that a certain proportion lie in a given region of the complex plane. Using an equivalent formulation as an obstacle problem, we describe the optimal distribution and some of its monotonicity properties.
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Armstrong, S.N., Serfaty, S. & Zeitouni, O. Remarks on a Constrained Optimization Problem for the Ginibre Ensemble. Potential Anal 41, 945–958 (2014). https://doi.org/10.1007/s11118-014-9402-0
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DOI: https://doi.org/10.1007/s11118-014-9402-0