On the multiplication of free $n$-tuples of non-commutative random variables

Details On the multiplication of free $n$-tuples of non-commutative random variables On the multiplication of free $n$-tuples of non-commutative random variables

1996-04-30

arxiv.org/abs/funct-an/9604011v1

Mathematics

Operator Algebras

LaTeX2e, Appendix upon request, to appear in Amer. J. Math

Scientific paper

Let $a_{1},...,a_{n}, b_{1},...,b_{n}$ be random variables in some (non-commutative) probability space, such that $\{a_{1}, ..., a_{n} \}$ is free from $\{b_{1}, ..., b_{n} \}$. We show how the joint distribution of the $n$-tuple $(a_{1} b_{1}, ..., a_{n} b_{n})$ can be described in terms of the joint distributions of $(a_{1}, ..., a_{n})$ and $(b_{1}, >..., b_{n})$, by using the combinatorics of the $n$-dimensional $R$-transform. We point out a few applications that can be easily derived from our result, concerning the left-and-right translation with a semicircular element (see Sections 1.6-1.10) and the compression with a projection (see Sections 1.11-1.14) of an $n$-tuple of non-commutative random variables. A different approach to two of these applications is presented by Dan Voiculescu in an Appendix to the paper.

Affiliated with

Also associated with

No associations

Rating

On the multiplication of free $n$-tuples of non-commutative random variables does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the multiplication of free $n$-tuples of non-commutative random variables, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the multiplication of free $n$-tuples of non-commutative random variables will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-502092