Non-Asymptotic Theory of Random Matrices

Non-asymptotic theory of random matrices: extreme singular values

The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to information theory operate with random matrices in fixed dimensions. This survey addresses the non-asymptotic theory of extreme singular values of random matrices w...

Non-Asymptotic Theory of Random Matrices Lecture 19: Small Ball Probability via Sum-Sets

Acceptable random variables in non-commutative probability spaces

Acceptable random variables are defined in noncommutative (quantum) probability spaces and some of probability inequalities for these classes  are obtained. These results are a generalization of negatively orthant dependent random variables in probability theory. Furthermore, the obtained results can be used for random matrices.

Non-Asymptotic Theory of Random Matrices

We will estimate the size of a random process (X t) t∈T by the size of another (simpler) random process (Y t) t∈T. Define a Gaussian centered process to be when X t is a mean-zero random variable. For a random variable X

An Application of Random Matrix Theory: Asymptotic Capacity of Ergodic and Non-ergodic Multiantenna Channels

Random matrices have fascinated mathematicians and physicists since they were first introduced in mathematical statistics by Wishart in 1928. The landmark contributions of Wishart, Wigner and later Marc̆enko-Pastur (in 1967) were motivated to a large extent by practical problems. Nowadays, random matrices find applications in fields as diverse as the Riemann hypothesis, stochastic differential e...