Séminaire Lotharingien de Combinatoire, B39c (1997), 38pp.

Roland Speicher

Free Probability Theory and Non-Crossing Partitions

Survey paper, on special invitation

Abstract. Voiculescu's free probability theory -- which was introduced in an operator algebraic context, but has since then developed into an exciting theory with a lot of links to other fields -- has an interesting combinatorial facet: it can be described by the combinatorial concept of multiplicative functions on the lattice of non-crossing partitions. In this survey I want to explain this connection -- without assuming any knowledge neither on free probability theory nor on non-crossing partitions.

Received: November 6, 1997; Accepted: January 27, 1998.

The following versions are available: