On multiplicative conditionally free convolution

2008/05/02 by Mihai Popa, Popa, Mihai, Jiun-Chau Wang +1
Mathematics · #05A18 #46L53 #60E07 #Advanced Operator Algebra Research #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Operator Algebras (math.OA) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.0805.0257

openalex publication_date 2008/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using the combinatorics of non-crossing partitions, we construct a conditionally free analogue of the Voiculescu's S-transform. The result is applied to analytical description of conditionally free multiplicative convolution and characterization of infinite divisibility.

Citations

• Limit laws for boolean convolutions

Related

• Convolution and Limit Theorems for Conditionally Free Random Variables
• Combinatorics of cyclic-conditional freeness
• Free multiplicative convolution with an arbitrary measure on the real line
• Multiplicative Monotone Convolution
• Non-crossing linked partitions and multiplication of free random variables