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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...
Stein's method and the multivariate CLT for traces of powers on the classical compact groups
random matrices compact Lie groups Haar measure traces of powers Stein’s method
2011/2/22
Let Mn be a random element of the unitary, special orthogonal, or unitary symplectic groups, distributed according to Haar measure. By a classical result of Diaconis and Shahshahani, for large matrix ...
CLT for the proportion of infected incividuals for an epidemic model on a complete graph
CLT epidemic model complete graph
2010/11/22
We prove a Central Limit Theorem for the proportion of infected individuals for an epidemic model by dealing with a discrete time system of simple random walks on a complete graph with n vertices. Ea...
CLT for spectra of submatrices of Wigner random matrices II. Stochastic evolution
CLT submatrices Wigner random matrices II Stochastic evolution
2010/11/22
We show that the global fluctuations of spectra of GOE and GUE matrices and their principal submatrices executing Dyson's Brownian motion are Gaussian in the limit of large matrix dimensions. For nest...
The Non Uniform Bounds of Remainder Term in CLT for the Sum of Functions of Uniform Spacings
Remainder Term Uniform Spacings
2010/3/4
The non uniform bound of the remainder in the central limit theorem for the sums of functions of uniform spacings is established. The bound depend on the moments of functions of the standard exponenti...