Boolean convolution of probability measures on the unit circle

Abstract

We introduce the boolean convolution for probability measures on the unit circle. Roughly speaking, it describes the distribution of the product of two boolean independent unitary random variables. We find an analogue of the characteristic function and determine all infinitely divisible probability measures on the unit circle for the boolean convolution.

13 pages, to appear in volume 15 of Seminaires et Congres

Cited by in corpus (10)

• Monotone and Boolean Convolutions for Non-compactly Supported Probability Measures
• Complex analysis methods in noncommutative probability
• An Operad of Non-commutative Independences Defined by Trees
• A new proof for the multiplicative property of the boolean cumulants with applications to operator-valued case
• Conditionally monotone independence and the associated products of graphs
• Bi-Boolean independence for pairs of algebras
• On multiplicative conditionally free convolution
• Appell polynomials and their relatives III. Conditionally free theory
• Additive processes on the unit circle and Loewner chains
• Conditionally monotone independence I: Independence, additive convolutions and related convolutions