Georgia Institute of Technology College of Sciences

We will present probability inequalities for the sums of independent, selfadjoint random matrices. The focus is made on noncommutative generalizations of the classical bounds of Azuma, Bernstein, Cherno ff, Hoeffding, among others. These inequalities imply concentration results for the empirical covariance matrices. No preliminary knowledge of probability theory will be assumed. (The talk is based on a paper by J. Tropp).