Combinatorics of the multiplicative conditionally free convolution
by
Mihai Popa
IMAR/University of Indiana at Bloomington

Using the combinatorics of non-crossing partitions, we construct

a conditionally free analogue of the Voiculescu’s S-transform. The result

is applied

to analytical description of conditionally free multiplicative convolution

and characterization of infinite divisibility.

Moreover, it is shown the role played by the non-crossing linked partitions,

introduced by K, Dykema in computing the coefficients of the S-transform and its

conditionally free analogue.

Date received: May 23, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawh-56.