Remarks on a constrained optimization problem for the Ginibre ensemble

2013/04/07 by Scott N. Armstrong, Armstrong, Scott N., Stéphane Serfaty +3 · 3 citations
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.1304.1964

openalex publication_date 2013/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• A direct approach to soft and hard edge universality for random normal matrices
• The Ginibre Ensemble Conditioned on an Overcrowding Event
• Electrostatic computations for statistical mechanics and random matrix applications

Related

• Remarks on the thin obstacle problem and constrained Ginibre ensembles
• The Ginibre Ensemble Conditioned on an Overcrowding Event
• Edge distribution of thinned real eigenvalues in the real Ginibre ensemble
• Limiting eigenvalue distribution of the general deformed Ginibre ensemble
• Limit Theorems For Non-Hermitian Ensembles