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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.

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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