Central Limit Theorem for Linear Eigenvalue Statistics of Elliptic Random Matrices

Sean O’Rourke () and David Renfrew ()
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Sean O’Rourke: University of Colorado at Boulder
David Renfrew: UCLA

Journal of Theoretical Probability, 2016, vol. 29, issue 3, 1121-1191

Abstract: 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 (Ann Probab 34(6):2118–2143, 2006) to real iid random matrices.

Keywords: Random matrices; Linear eigenvalue statistics; Central limit theorem; Elliptic random matrices; 60B20; 60F05 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10959-015-0609-9

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