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Linear Statistics of Non-Hermitian Matrices Matching the Real or Complex Ginibre
Ensemble to Four Moments
Published Web Location
https://arxiv.org/pdf/1510.02987.pdfNo data is associated with this publication.
Abstract
We prove that, for general test functions, the limiting behavior of the linear statistic of an independent entry random matrix is determined only by the first four moments of the entry distributions. This immediately generalizes the known central limit theorem for independent entry matrices with complex normal entries. We also establish two central limit theorems for matrices with real normal entries, considering separately functions supported exclusively on and exclusively away from the real line. In contrast to previously obtained results in this area, we do not impose analyticity on test functions.