Linear Statistics of Non-Hermitian Matrices Matching the Real or Complex Ginibre Ensemble to Four Moments

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.

Preliminary version

References in corpus (2)

• Central limit theorem for linear eigenvalue statistics of random matrices with independent entries
• Central Limit Theorem for linear eigenvalue statistics of the Wigner and sample covariance random matrices

Cited by in corpus (5)

• Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble
• On the number of real eigenvalues of a product of truncated orthogonal random matrices
• On the Correlation Functions of the Characteristic Polynomials of Non-Hermitian Random Matrices with Independent Entries
• How many eigenvalues of a product of truncated orthogonal matrices are real?
• Central limit theorems for the real eigenvalues of large Gaussian random matrices