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A CLT for information-theoretic statistics of Gram random matrices with a given variance profile. (English) Zbl 1166.15013
The authors consider an \(N\times n\) random matrix \(Y_n\) with entries given by \(Y_{ij}^n=\sigma_{ij}(n)X_{ij}^n/\sqrt{n}\), the \(X_{ij}^n\) being centered, independent and identically distributed random variables. They study the fluctuations of the random variable
\[ \log\det (Y_nY^*_n+\rho I_N) \] and prove that under proper scaling, this random variable satisfies a central limit theorem. Such a central limit theorem is of interest in the field of wireless communications and random matrix theory.

15B52 Random matrices (algebraic aspects)
15A18 Eigenvalues, singular values, and eigenvectors
60F05 Central limit and other weak theorems
Full Text: DOI
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