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Remarks on a Constrained Optimization Problem for the Ginibre Ensemble |
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| Authors: | Scott N. Armstrong Sylvia Serfaty Ofer Zeitouni |
| Affiliation: | 1. CEREMADE (UMR CNRS 7534), Université Paris-Dauphine, Paris, France 2. Laboratoire Jacques Louis Lions, UPMC Paris 6, Paris, France 3. The Courant Institute of Mathematical Sciences, New York University, New York, NY, USA 4. Faculty of Mathematics, Weizmann Institute of Science, Rehovot, 76100, Israel |
| 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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