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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.

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