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- W2950978046 abstract "Consider a $Ntimes n$ random matrix $Y_n=(Y_{ij}^{n})$ where the entries are given by $$ Y_{ij}^{n}=frac{sigma_{ij}(n)}{sqrt{n}} X_{ij}^{n} $$ the $X_{ij}^{n}$ being centered, independent and identically distributed random variables with unit variance and $(sigma_{ij}(n); 1le ile N, 1le jle n)$ being an array of numbers we shall refer to as a variance profile. We study in this article the fluctuations of the random variable $$ logdet(Y_n Y_n^* + rho I_N) $$ where $Y^*$ is the Hermitian adjoint of $Y$ and $rho > 0$ is an additional parameter. We prove that when centered and properly rescaled, this random variable satisfies a Central Limit Theorem (CLT) and has a Gaussian limit whose parameters are identified. A complete description of the scaling parameter is given; in particular it is shown that an additional term appears in this parameter in the case where the 4$^textrm{th}$ moment of the $X_{ij}$'s differs from the 4$^{textrm{th}}$ moment of a Gaussian random variable. Such a CLT is of interest in the field of wireless communications." @default.
- W2950978046 created "2019-06-27" @default.
- W2950978046 creator A5052471480 @default.
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- W2950978046 date "2008-01-01" @default.
- W2950978046 modified "2023-09-23" @default.
- W2950978046 title "A CLT for Information-theoretic statistics of Gram random matrices with a given variance profile" @default.
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