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Central limit theorem for linear eigenvalue statistics of elliptic random matrices (1410.4586v2)
Published 16 Oct 2014 in math.PR, math-ph, and math.MP
Abstract: We consider a class of elliptic random matrices which generalize two classical ensembles from random matrix theory: Wigner matrices and random matrices with iid entries. In particular, we establish a central limit theorem for linear eigenvalue statistics of real elliptic random matrices under the assumption that the test functions are analytic. As a corollary, we extend the results of Rider and Silverstein to real iid random matrices.