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Universality results for the largest eigenvalues of some sample covariance matrix ensembles
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  • Published: 08 January 2008

Universality results for the largest eigenvalues of some sample covariance matrix ensembles

  • Sandrine Péché1 nAff2 

Probability Theory and Related Fields volume 143, pages 481–516 (2009)Cite this article

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Abstract

For sample covariance matrices with i.i.d. entries with sub-Gaussian tails, when both the number of samples and the number of variables become large and the ratio approaches one, it is a well-known result of Soshnikov that the limiting distribution of the largest eigenvalue is same that of Gaussian samples. In this paper, we extend this result to two cases. The first case is when the ratio approaches an arbitrary finite value. The second case is when the ratio becomes infinite or arbitrarily small.

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Author notes
  1. Sandrine Péché

    Present address: Department of Mathematics, University of California at Davis, One Shields Ave., Davis, CA, 95616, USA

Authors and Affiliations

  1. Institut Fourier BP 74, 100 Rue des maths, 38402, Saint Martin d’Heres, France

    Sandrine Péché

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  1. Sandrine Péché
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Correspondence to Sandrine Péché.

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Péché, S. Universality results for the largest eigenvalues of some sample covariance matrix ensembles. Probab. Theory Relat. Fields 143, 481–516 (2009). https://doi.org/10.1007/s00440-007-0133-7

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  • Received: 03 October 2007

  • Revised: 05 December 2007

  • Published: 08 January 2008

  • Issue Date: March 2009

  • DOI: https://doi.org/10.1007/s00440-007-0133-7

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Keywords

  • Large Eigenvalue
  • Sample Covariance
  • Oriented Edge
  • Typical Path
  • Marked Vertex
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