Free probability for pairs of faces III: 2-Variables bi-free partial S- and T-transforms

Multilinear Function Series and Transforms in Free Probability Theory

The algebra Mul[[B]] of formal multilinear function series over an algebra B and its quotient SymMul[[B]] are introduced, as well as corresponding operations of formal composition, which are associative. In the setting of Mul[[B]], the unsymmetrized R– and T–transforms of random variables in B–valued noncommutative probability spaces are introduced. These satisfy properties analogous to the usu...

FREE SEMIGROUPS AND IDEMPOTENTS IN T

The known theory for an oid T shows how to find a subset T of ?T, which is a compact right topological semigroup [I]. The success of the methods in [2] for obtaining properties of-T has prompted us to see how successful they would be in another context. Thus we find (Theorem 4.8) that T cont ains copies of free semigroups on 2? generators, is an immediate consequence of the stronger resu...

Free Probability for Probabilists

This is an introduction to some of the most probabilistic aspects of free probability theory.

Free Involutions on S 2 × S 3

In this paper, an explicit classification of smooth free involutions on S×S up to conjugation is obtained.

Free Probability Theory and Free Diffusion