Multilinear function series and transforms in free probability theory Academic Article

abstract

• 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.

authors

• Dykema, Kenneth

published proceedings

• ADVANCES IN MATHEMATICS

author list (cited authors)

• Dykema, K. J.

citation count

• 22

complete list of authors

• Dykema, Kenneth J

publication date

• January 2007

publisher

• Elsevier  Publisher

published in

• Advances in Mathematics  Journal

keywords

• Free Convolution
• Multilinear Function Series
• Noncrossing Linked Partitions
• Noncrossing Partitions
• R-transform
• S-transform
• T-transform

Digital Object Identifier (DOI)

• 10.1016/j.aim.2006.02.011

start page

• 351

end page

• 407

volume

• 208

issue

• 1

URL

• http%3A%2F%2Fdx.doi.org%2F10.1016%2Fj.aim.2006.02.011