Geodesic
Free Probability Theory and Non-Crossing Partitions
Séminaire lotharingien de combinatoire, Tome 39 (1997) 
Roland Speicher. Free Probability Theory and Non-Crossing Partitions. Séminaire lotharingien de combinatoire, Tome 39 (1997). http://geodesic.mathdoc.fr/item/SLC_1997_39_a2/
@article{SLC_1997_39_a2,
     author = {Roland Speicher},
     title = {Free {Probability} {Theory} and {Non-Crossing} {Partitions}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {1997},
     volume = {39},
     url = {http://geodesic.mathdoc.fr/item/SLC_1997_39_a2/}
}
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AU  - Roland Speicher
TI  - Free Probability Theory and Non-Crossing Partitions
JO  - Séminaire lotharingien de combinatoire
PY  - 1997
VL  - 39
UR  - http://geodesic.mathdoc.fr/item/SLC_1997_39_a2/
ID  - SLC_1997_39_a2
ER  - 
%0 Journal Article
%A Roland Speicher
%T Free Probability Theory and Non-Crossing Partitions
%J Séminaire lotharingien de combinatoire
%D 1997
%V 39
%U http://geodesic.mathdoc.fr/item/SLC_1997_39_a2/
%F SLC_1997_39_a2

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

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.