Multilinear function series and transforms in free probability theory Academic Article uri icon


  • The algebra Mul {left open bracket} B {right open bracket} of formal multilinear function series over an algebra B and its quotient SymMul {left open bracket} B {right open bracket} are introduced, as well as corresponding operations of formal composition. In the setting of Mul {left open bracket} B {right open bracket}, the unsymmetrized R- and T-transforms of random variables in B-valued noncommutative probability spaces are introduced. These satisfy properties analogous to the usual R- and T-transforms (the latter being just the reciprocal of the S-transform), but describe all moments of a random variable, not only the symmetric moments. The partially ordered set of noncrossing linked partitions is introduced and is used to prove properties of the unsymmetrized T-transform. 2006 Elsevier Inc. All rights reserved.

published proceedings


author list (cited authors)

  • Dykema, K. J.

citation count

  • 22

complete list of authors

  • Dykema, Kenneth J

publication date

  • January 2007