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A CLT for Information-theoretic statistics of Non-centered Gram random matrices
Random Matrix Spectral measure Stieltjes Transform Central Limit Theorem
2011/8/22
Abstract: In this article, we study the fluctuations of the random variable: $$ {\mathcal I}_n(\rho) = \frac 1N \log\det(\Sigma_n \Sigma_n^* + \rho I_N),\quad (\rho>0) $$ where $\Sigma_n= n^{-1/2} D_n...
Limit distribution in the $q$-CLT for $q \ge 1$ can not have a compact support
q-central limit theorem q-Fourier transform q-Gaussian
2011/3/2
In a recent paper Hilhorst (1) illustrated that the q-Fourier transform for q > 1 is not
invertible in the space of density functions. Using an invariance principle he constructed a
family of densit...