NCDFP · Non-Commutative Distributions in Free Probability

We intend to study new directions in free probability theory with high potential to lead to breakthroughs in our understanding of random matrix models and operator algebras. We will drive forward the study of ""free analysis"" which is intended to provide a whole new mathematical theory for variables with the highest degree of non-commutativity and which lies at the crossroad of many exciting mathematical subjects.More specifically, the objective of the proposal is to extend our armory for dealing with non-commutative distributions and to attack some of the fundamental problems which are related to such distributions, like: the existence and properties of the limit of multi-matrix models