Random Operator-Valued Models: Combining Stochastic and Algebraic Models

Abstract

Usually, the most natural model for a multiantenna channel is of a stochastic nature. When the channel exhibits enough structural properties (e.g. symmetries), these stochastic models can be approximated using algebraic objects. An archetypical application of this paradigm comes from the fact that certain random matrices behave, in the limit, as operators in a non-commutative probability space. However, in some situations the structural properties of the channel account only for a part of the overall channel behavior. In this talk we will introduce a class of models that encode the structural properties of the channel using algebraic objects and, at the same time, capture the non-structured properties of the channel using stochastic objects. We will discuss some elementary properties of these models and how to handle them using both classical and free probabilistic tools.