TITLE

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

AUTHOR(S)
Shcherbina, T.
PUB. DATE
June 2013
SOURCE
Probability Theory & Related Fields;Jun2013, Vol. 156 Issue 1/2, p449
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
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 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.
ACCESSION #
87610037

 

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