Multilinear function series in conditionally free probability with amalgamation

2007/03/31 by Mihai Popa, Popa, Mihai
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #46L08 #46L53 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Probability and Risk Models #Random Matrices and Applications #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.0704.0040

openalex publication_date 2007/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Multilinear function series and transforms in free probability theory
• Convolution and Limit Theorems for Conditionally Free Random Variables
• Freeness with amalgamation, limit theorems and S-transform in non-commutative probability spaces of type B
• A combinatorial approach to monotonic independence over a C*-algebra
• A Characterization of Freeness by a Factorization Property of R-transform