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Central Limit Theorem for Linear Eigenvalue Statistics of Elliptic Random Matrices

Author

Listed:
  • Sean O’Rourke

    (University of Colorado at Boulder)

  • David Renfrew

    (UCLA)

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.

Suggested Citation

  • Sean O’Rourke & David Renfrew, 2016. "Central Limit Theorem for Linear Eigenvalue Statistics of Elliptic Random Matrices," Journal of Theoretical Probability, Springer, vol. 29(3), pages 1121-1191, September.
    • Handle: RePEc:spr:jotpro:v:29:y:2016:i:3:d:10.1007_s10959-015-0609-9
    DOI: 10.1007/s10959-015-0609-9
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    References listed on IDEAS

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    1. Pan, Guangming & Zhou, Wang, 2010. "Circular law, extreme singular values and potential theory," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 645-656, March.
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    Cited by:

    1. Natalie Coston & Sean O’Rourke, 2020. "Gaussian Fluctuations for Linear Eigenvalue Statistics of Products of Independent iid Random Matrices," Journal of Theoretical Probability, Springer, vol. 33(3), pages 1541-1612, September.

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    1. Natalie Coston & Sean O’Rourke, 2020. "Gaussian Fluctuations for Linear Eigenvalue Statistics of Products of Independent iid Random Matrices," Journal of Theoretical Probability, Springer, vol. 33(3), pages 1541-1612, September.
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