Mixtures of classical and free independence

Abstract

We revive the concept of Lambda-freeness of Mlotkowski, which describes a mixture of classical and free independence between algebras of random variables. In particular, we give a description of this in terms of cumulants; this will be instrumental in the subsequent paper [SW] where the quantum symmetries underlying these mixtures of classical and free independences will be considered.

We rewrote and shortened the earlier version. The third version contains mainly the results which are new compared to the paper of Mlotkowski