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Remarks on a constrained optimization problem for the Ginibre ensemble. (English) Zbl 1300.31004
Summary: 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.

MSC:
31A35 Connections of harmonic functions with differential equations in two dimensions
49K10 Optimality conditions for free problems in two or more independent variables
60B20 Random matrices (probabilistic aspects)
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