Mathematical Foundations for Signal Processing, Communications, and Networking

Chapter 8    Random Matrix Theory

Romain Couillet^‡ and Merouane Debbah^‡

^‡ L’École Supérieure D’Electricité (SUPELEC), France

Random matrix theory deals with the study of matrix-valued random variables. It is conventionally considered that random matrix theory dates back to the work of Wishart in 1928 [1] on the properties of matrices of the type XX^† with X ∈ ℂ^N×n a random matrix with independent Gaussian entries with zero mean and equal variance. Wishart and his followers were primarily interested in the joint distribution of the entries of such matrices and then on their eigenvalues distribution. It then dawned to mathematicians that, as the matrix dimensions N and n grow large with ratio converging to a positive value, its eigenvalue distribution ...