Free probability

Summary

Free probability is a theory of noncommuting random variables in which the classical notion of independence is replaced by free independence. It was introduced by Dan Voiculescu in the 1980s to study the von Neumann algebras of free groups. It has analogues of the central limit theorem, of convolution and of cumulants. In it the Wigner semicircle law plays the role of the normal distribution. It also describes the limit of large random matrices, which become asymptotically free.