Multilinear function series in conditionally free probability with amalgamation

Multilinear Function Series in Conditionally Free Probability with Amalgamation

As in the cases of freeness and monotonic independence, the notion of conditional freeness is meaningful when complex-valued states are replaced by positive conditional expectations. In this framework, the paper presents several positivity results, a version of the central limit theorem and an analogue of the conditionally free R-transform constructed by means of multilinear function series.

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...

Notes on C-free Probability with Amalgamation

As in the cases of freeness and monotonic independence, the notion of conditional freeness is meaningful when complex-valued states are replaced by positive conditional expectations. In this framework, the paper presents several positivity results, a version of the central limit theorem and an analogue of the conditionally free R-transform constructed by means of multilinear function series.

Conditionally Invariant Probability Measures

V eronique Maume-Deschamps Section de Math ematiques, Universit e de Gen eve 2-4 rue du Lievre CP 240 Suisse. Abstract Let T be a measurable map on a Polish space X, let Y be a non trivial subset of X. We give conditions ensuring existence of conditionally invariant probability measures (to non absorption in Y). We also supply suucient conditions for these probability measures to be absolutely ...

Free Products with Amalgamation and 3-manifolds