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Outliers in the spectrum of iid matrices with bounded rank perturbations
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  • Published: 03 November 2011

Outliers in the spectrum of iid matrices with bounded rank perturbations

  • Terence Tao1 

Probability Theory and Related Fields volume 155, pages 231–263 (2013)Cite this article

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An Erratum to this article was published on 28 June 2013

Abstract

It is known that if one perturbs a large iid random matrix by a bounded rank error, then the majority of the eigenvalues will remain distributed according to the circular law. However, the bounded rank perturbation may also create one or more outlier eigenvalues. We show that if the perturbation is small, then the outlier eigenvalues are created next to the outlier eigenvalues of the bounded rank perturbation; but if the perturbation is large, then many more outliers can be created, and their law is governed by the zeroes of a random Laurent series with Gaussian coefficients. On the other hand, these outliers may be eliminated by enforcing a row sum condition on the final matrix.

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Authors and Affiliations

  1. Department of Mathematics, UCLA, Los Angeles, CA, 90095-1555, USA

    Terence Tao

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  1. Terence Tao
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Corresponding author

Correspondence to Terence Tao.

Additional information

T. Tao is is supported by a grant from the MacArthur Foundation, by NSF grant DMS-0649473, and by the NSF Waterman award.

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Tao, T. Outliers in the spectrum of iid matrices with bounded rank perturbations. Probab. Theory Relat. Fields 155, 231–263 (2013). https://doi.org/10.1007/s00440-011-0397-9

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  • Received: 21 December 2010

  • Revised: 07 July 2011

  • Published: 03 November 2011

  • Issue Date: February 2013

  • DOI: https://doi.org/10.1007/s00440-011-0397-9

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Mathematics Subject Classification (2000)

  • 60B20
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