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Capacity of Finite State Channels Based on Lyapunov Exponents of Random Matrices
Finite-state channel hidden Markov model random matrices Shannon capacity
2015/7/6
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...
Distribution of the largest eigenvalue for real Wishart and Gaussian random matrices and a simple approximation for the Tracy-Widom distribution
Random Matrix Theory characteristic roots largest eigenvalue Tracy-Widom Distribution Wishart Matrices Gaussian Orthogonal Ensemble
2012/11/23
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-...
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...
A Subspace Estimator for Fixed Rank Perturbations of Large Random Matrices
Large Random Matrix Theory MUSIC Algorithm Extreme Eigenvalues
2011/7/6
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...
Limiting Laws of Coherence of Random Matrices with Applications to Testing Covariance Structure and Construction of Compressed Sensing Matrices
Chen-Stein method coherence compressed sensing matrix covariance struc-ture law of large numbers limiting distribution maxima moderate deviations mutual incoherence property random matrix sample correlation matrix
2011/3/21
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...
Limiting Laws of Coherence of Random Matrices with Applications to Testing Covariance Structure and Construction of Compressed Sensing Matrices
Chen-Stein method coherence compressed sensing matrix covariance struc-ture law of large numbers limiting distribution maxima moderate deviations mutual incoherence property random matrix sample correlation matrix
2011/3/23
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...
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...
Large deviations and stochastic calculus for large random matrices
large deviations random matrices non-commutative measure integration.
2009/5/18
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...
Poisson Statistics for the Largest Eigenvalues of Wigner Random Matrices with Heavy Tails
random matrices largest eigenvalues Poisson statistics
2009/4/28
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.
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...
On the lower bound of the spectral norm of symmetric random matrices with independent entries
spectral norm random symmetric matrix
2009/3/20
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 ...
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...