1994/10/17 by Marek Bożejko, Bozejko, Marek, Michael Leinert +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.funct-an/9410004
openalex publication_date 1994/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the notion of a conditionally free product and conditionally free convolution. We describe this convolution both from a combinatorial point of view, by showing its connection with the lattice of non-crossing partitions, and from an analytic point of view, by presenting the basic formula for its R-transform. We calculate explicitly the distributions of the conditionally free Gaussian and conditionally free Poisson distribution.