This summary will briefly describe some recent results in random matrix theory and their applications. 1 Motivation 1.1 Multiple Antenna Gaussian Channels 1.1.1 The deterministic case Consider a gaussian channel with t transmitting and r receiving antennas. The received vector y ∈Cr will depend on the transmitted vector x ∈Ct by y = Hx+n where H is an rxt complex matrix of gains and n is a vect...

which is the Central Limit Theorem. In principle, all the random variables X1, X2, · · · , XN can be of order 1, hence SN ∼ 1 as well, but the probability of having such a rare event is incredibly small. We can even estimate the bound on the probability for the rare event from the large deviation principle. A similar phenomenon happens when we form a large matrix from i.i.d. random variables an...

We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted averages of the corresponding quantities in the standard theory assuming that the mean level spacing itself is a stochastic variable. We illustrate the meth...

In this preface to the Journal of Physics A, Special Edition on Random Matrix Theory, we give a review of the main historical developments of random matrix theory. A short summary of the papers that appear in this special edition is also given.

This handout provides the essential elements needed to understand finite random matrix theory. A cursory observation should reveal that the tools for infinite random matrix theory are quite different from the tools for finite random matrix theory. Nonetheless, there are significantly more published applications that use finite random matrix theory as opposed to infinite random matrix theory. Ou...

The focus of this paper is to consider the compressed sensing problem. It is stated that the compressed sensing theory, under certain conditions, helps relax the Nyquist sampling theory and takes smaller samples. One of the important tasks in this theory is to carefully design measurement matrix (sampling operator). Most existing methods in the literature attempt to optimize a randomly initiali...