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A CLT for Information-theoretic statistics of Non-centered Gram random matrices
Random Matrix Spectral measure Stieltjes Transform
2011/7/19
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^{1/2} X_n...
The spectrum of kernel random matrices
spectrum kernel random matrices high-dimensional statisticalinference
2010/3/9
We place ourselves in the setting of high-dimensional statistical
inference where the number of variables p in a dataset of interest is
of the same order of magnitude as the number of observations n...
Wigner theorems for random matrices with dependent entries：Ensembles associated to symmetric spaces and sample covariance matrices
Wigner theorem symmetric space sample covariance
2009/3/20
It is a classical result of Wigner that for an hermitian matrix with independent entries on and above the diagonal, the mean empirical eigenvalue distribution converges weakly to the semicircle law as...
Concentration of the Spectral Measure for Large Random Matrices with Stable Entries
Spectral Measure Random Matrices Infinitely divisibility Stable Vector Concentration
2010/4/29
We derive concentration inequalities for functions of the empirical
measure of large random matrices with infinitely divisible entries and,
in particular, stable ones. We also give concentration res...
Learning Trigonometric Polynomials from Random Samples and Exponential Inequalities for Eigenvalues of Random Matrices
eigenvalues exponential inequality learning theory randommatrix random sampling
2010/4/26
Motivated by problems arising in random sampling of trigonometric polynomials,
we derive exponential inequalities for the operator norm of the difference
between the sample second moment matrix n...