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On the correlation functions of the characteristic polynomials of the hermitian sample covariance matrices
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  • Published: 27 May 2012

On the correlation functions of the characteristic polynomials of the hermitian sample covariance matrices

  • T. Shcherbina1 

Probability Theory and Related Fields volume 156, pages 449–482 (2013)Cite this article

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Abstract

We consider asymptotic behavior of the correlation functions of the characteristic polynomials of the hermitian sample covariance matrices \({H_n=n^{-1}A_{m,n}^* A_{m,n}}\), where A m,n is a m × n complex random matrix with independent and identically distributed entries \({\mathfrak{R}a_{\alpha j}}\) and \({\mathfrak{I}a_{\alpha j}}\). We show that for the correlation function of any even order the asymptotic behavior in the bulk and at the edge of the spectrum coincides with those for the Gaussian Unitary Ensemble up to a factor, depending only on the fourth moment of the common probability law of entries \({\mathfrak{R}a_{\alpha j}}\), \({\mathfrak{I}a_{\alpha j}}\), i.e., the higher moments do not contribute to the above limit.

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Authors and Affiliations

  1. Institute for Low Temperature Physics, 47 Lenin Ave., 61103, Kharkov, Ukraine

    T. Shcherbina

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  1. T. Shcherbina
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Correspondence to T. Shcherbina.

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Shcherbina, T. On the correlation functions of the characteristic polynomials of the hermitian sample covariance matrices. Probab. Theory Relat. Fields 156, 449–482 (2013). https://doi.org/10.1007/s00440-012-0433-4

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  • Received: 15 July 2011

  • Revised: 23 April 2012

  • Published: 27 May 2012

  • Issue Date: June 2013

  • DOI: https://doi.org/10.1007/s00440-012-0433-4

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Mathematics Subject Classification

  • Primary 15B52
  • Secondary 15B57
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