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183
On the capacity of spatially correlated MIMO Rayleighfading channels
 IEEE Trans. Inform. Theory
, 2003
"... Abstract—In this paper, we investigate the capacity distribution of spatially correlated, multipleinput–multipleoutput (MIMO) channels. In particular, we derive a concise closedform expression for the characteristic function (c.f.) of MIMO system capacity with arbitrary correlation among the tran ..."
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Cited by 134 (15 self)
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Abstract—In this paper, we investigate the capacity distribution of spatially correlated, multipleinput–multipleoutput (MIMO) channels. In particular, we derive a concise closedform expression for the characteristic function (c.f.) of MIMO system capacity with arbitrary correlation among the transmitting antennas or among the receiving antennas in frequencyflat Rayleighfading environments. Using the exact expression of the c.f., the probability density function (pdf) and the cumulative distribution function (CDF) can be easily obtained, thus enabling the exact evaluation of the outage and mean capacity of spatially correlated MIMO channels. Our results are valid for scenarios with the number of transmitting antennas greater than or equal to that of receiving antennas with arbitrary correlation among them. Moreover, the results are valid for an arbitrary number of transmitting and receiving antennas in uncorrelated MIMO channels. It is shown that the capacity loss is negligible even with a correlation coefficient between two adjacent antennas as large as 0 5 for exponential correlation model. Finally, we derive an exact expression for the mean value of the capacity for arbitrary correlation matrices. Index Terms—Eigenvalues distribution, multiple input–multiple output (MIMO), multiple antennas, Rayleighfading channels, Shannon capacity, Wishart matrices. I.
Logarithmic concave measures with application to . . .
 ACTA SCIENTIARUM MATHEMATICARUM, 32 (1971), PP. 301–316.
, 1971
"... ..."
Concentration of the Spectral Measure for Large Matrices
 ELECTRONIC COMMUNICATIONS IN PROBABILITY
, 2000
"... We derive concentration inequalities for functions of the empirical measure of eigenvalues for large, random, self adjoint matrices, with not necessarily Gaussian entries. The results presented apply in particular to nonGaussian Wigner and Wishart matrices. We also provide concentration bounds fo ..."
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Cited by 103 (14 self)
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We derive concentration inequalities for functions of the empirical measure of eigenvalues for large, random, self adjoint matrices, with not necessarily Gaussian entries. The results presented apply in particular to nonGaussian Wigner and Wishart matrices. We also provide concentration bounds for noncommutative functionals of random matrices.
Random matrix theory
, 2005
"... Random matrix theory is now a big subject with applications in many disciplines of science, engineering and finance. This article is a survey specifically oriented towards the needs and interests of a numerical analyst. This survey includes some original material not found anywhere else. We includ ..."
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Cited by 80 (4 self)
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Random matrix theory is now a big subject with applications in many disciplines of science, engineering and finance. This article is a survey specifically oriented towards the needs and interests of a numerical analyst. This survey includes some original material not found anywhere else. We include the important mathematics which is a very modern development, as well as the computational software that is transforming the theory into useful practice.
Orthogonal polynomial ensembles in probability theory
 Prob. Surv
, 2005
"... Abstract: We survey a number of models from physics, statistical mechanics, probability theory and combinatorics, which are each described in terms of an orthogonal polynomial ensemble. The most prominent example is apparently the Hermite ensemble, the eigenvalue distribution of the Gaussian Unitary ..."
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Cited by 63 (1 self)
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Abstract: We survey a number of models from physics, statistical mechanics, probability theory and combinatorics, which are each described in terms of an orthogonal polynomial ensemble. The most prominent example is apparently the Hermite ensemble, the eigenvalue distribution of the Gaussian Unitary Ensemble (GUE), and other wellknown ensembles known in random matrix theory like the Laguerre ensemble for the spectrum of Wishart matrices. In recent years, a number of further interesting models were found to lead to orthogonal polynomial ensembles, among which the corner growth model, directed last passage percolation, the PNG droplet, noncolliding random processes, the length of the longest increasing subsequence of a random permutation, and others. Much attention has been paid to universal classes of asymptotic behaviors of these models in the limit of large particle numbers, in particular the spacings between the particles and the fluctuation behavior of the largest particle. Computer simulations suggest that the connections go even farther
From the LittlewoodOfford problem to the Circular Law: Universality of the spectral distribution of random matrices
 BULL. AMER. MATH. SOC
, 2009
"... The famous circular law asserts that if Mn is an n×n matrix with iid complex entries of mean zero and unit variance, then the empirical spectral distribution of the normalized matrix 1 √ Mn converges both in probability and n almost surely to the uniform distribution on the unit disk {z ∈ C: z  ≤1 ..."
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Cited by 53 (7 self)
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The famous circular law asserts that if Mn is an n×n matrix with iid complex entries of mean zero and unit variance, then the empirical spectral distribution of the normalized matrix 1 √ Mn converges both in probability and n almost surely to the uniform distribution on the unit disk {z ∈ C: z  ≤1}. After a long sequence of partial results that verified this law under additional assumptions on the distribution of the entries, the circular law is now known to be true for arbitrary distributions with mean zero and unit variance. In this survey we describe some of the key ingredients used in the establishment of the circular law at this level of generality, in particular recent advances in understanding the LittlewoodOfford problem and its inverse.
High dimensional statistical inference and random matrices
 IN: PROCEEDINGS OF INTERNATIONAL CONGRESS OF MATHEMATICIANS
, 2006
"... Multivariate statistical analysis is concerned with observations on several variables which are thought to possess some degree of interdependence. Driven by problems in genetics and the social sciences, it first flowered in the earlier half of the last century. Subsequently, random matrix theory ..."
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Cited by 49 (1 self)
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Multivariate statistical analysis is concerned with observations on several variables which are thought to possess some degree of interdependence. Driven by problems in genetics and the social sciences, it first flowered in the earlier half of the last century. Subsequently, random matrix theory (RMT) developed, initially within physics, and more recently widely in mathematics. While some of the central objects of study in RMT are identical to those of multivariate statistics, statistical theory was slow to exploit the connection. However, with vast data collection ever more common, data sets now often have as many or more variables than the number of individuals observed. In such contexts, the techniques and results of RMT have much to offer multivariate statistics. The paper reviews some of the progress to date.