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The finite-state Markov channel (FSMC) is a timevarying channel having states that are characterized by a finitestate Markov chain. These channels have infinite memory, which complicates their capacit...
We derive the exact distribution of the largest eigenvalue for finite dimensions real Wishart matrices and for the Gaussian Orthogonal Ensemble (GOE). We compare the exact distribution with the Tracy-...
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...
This paper deals with the problem of parameter estimation based on certain eigenspaces of the empirical covariance matrix of an observed multidimensional time series, in the case where the time series...
Kernel density estimation (KDE) is a popular statistical technique for estimating the underlying density distribution with minimal assumptions. Although they can be shown to achieve asymptotic estimat...
Testing covariance structure is of significant interest in many areas of statistical analysis and construction of compressed sensing matrices is an important problem in signal processing. Motivated b...
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...
Large random matrices appear in different fields of mathematics and physics such as combinatorics, probability theory, statistics, operator theory, number theory, quantum field theory, string theory e...
We study large Wigner random matrices in the case when the marginal distributions of matrix entries have heavy tails. We prove that the largest eigenvalues of such matrices have Poisson statistics.
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...
We show that the spectral radius of an N-dimensional random symmetric matrix with i.i.d. bounded centered but non-symmetrically distributed entries is bounded from below by 2σ - o(N-6/11+ε), where σ2 ...
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...
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...

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