correlation
Random matrices have fascinated mathematicians and physicists since they were first introduced in mathe- matical statistics by Wishart in 1928. After a slow start, the subject gained prominence when Wigner introduced the concept of statistical distribution of nuclear energy levels in 1950. Since then, random matrix theory has matured into a field with applications in many branches of physics and mathematics, and nowadays random matrices find applications in fields as diverse as the
Riemann hypothesis, stochastic differential equations, statistical physics, chaotic systems, numerical linear al- gebra, neural networks, etc. Recently random matrices are also finding an increasing number of applications in the context of information theory and signal processing, which include among others: wireless communications channels, learning and neural networks, capacity of ad hoc networks, direction of arrival estimation in sensor ar- rays, etc. The earliest applications to wireless communi- cation were the pioneering works of Foschini and Telatar in the mid-90s on characterizing the capacity of multi- antenna channels. With works like [1], [2], [3] which, ini- tially, called attention to the effectiveness of asymptotic random matrix theory in wireless communication theory, interest in the study of random matrices began and the singular value densities of random matrices and their asymptotics, as the matrix size tends to infinity, became an active research area in information/communication.
Theory of Large Dimensional Random Matrices for Engineers
Jack W. Silverstein
∗
Department of Mathematics, Box 8205,
North Carolina State University,
Raleigh, NC 27695-8205, USA,
Email: jack@math.ncsu.edu
Antonia M. Tulino
Dip. di Ing. Elettronica e delle Telecomunicazioni,
Universita’ degli Studi di Napoli, ”Fedrico I
Via Claudio 21, Napoli Italy,
Email: atulino@princeton.edu
Abstract
—In the last few years, the asymptotic distribu- tion of the
Riemann hypothesis, stochastic differential equations, statistical physics, chaotic systems, numerical linear al- gebra, neural networks, etc. Recently random matrices are also finding an increasing number of applications in the context of information theory and signal processing, which include among others: wireless communications channels, learning and neural networks, capacity of ad hoc networks, direction of arrival estimation in sensor ar- rays, etc. The earliest applications to wireless communi- cation were the pioneering works of Foschini and Telatar in the mid-90s on characterizing the capacity of multi- antenna channels. With works like [1], [2], [3] which, ini- tially, called attention to the effectiveness of asymptotic random matrix theory in wireless communication theory, interest in the study of random matrices began and the singular value densities of random matrices and their asymptotics, as the matrix size tends to infinity, became an active research area in information/communication.
Theory of Large Dimensional Random Matrices for Engineers
Jack W. Silverstein
∗
Department of Mathematics, Box 8205,
North Carolina State University,
Raleigh, NC 27695-8205, USA,
Email: jack@math.ncsu.edu
Antonia M. Tulino
Dip. di Ing. Elettronica e delle Telecomunicazioni,
Universita’ degli Studi di Napoli, ”Fedrico I
Via Claudio 21, Napoli Italy,
Email: atulino@princeton.edu
Abstract
—In the last few years, the asymptotic distribu- tion of the