Limit distributions of Gaussian block ensembles

It has been shown by Voiculescu that important classes of square independent random matrices are asymptotically free, where freeness is a noncommutative analog of classical independence. Recently, we introduced the concept of matricial freeness, which is similar to freeness in free probability, but it also has some matricial features. Using this new concept of noncommutative independence, we described the asymptotics of blocks and symmetric blocks of certain classes of independent random matrices. In this paper, we present the main results obtained in this framework, concentrating on the ensembles of blocks of Gaussian random matrices.