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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.

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