open access

https://hdl.handle.net/2115/76011

Conditionally monotone independence I: Independence, additive convolutions and related convolutions

英語

cumulants

2011-09

Infinite Dimensional Analysis, Quantum Probability and Related Topics

14(03)

465-516

We define a product of algebraic probability spaces equipped with two states. This product is called a conditionally monotone product. This product is a new example of independence in noncommutative probability theory and unifies the monotone and Boolean products, and moreover, the orthogonal product. Then we define the associated cumulants and calculate the limit distributions in central limit theorem and Poisson's law of small numbers. We also prove a combinatorial moment-cumulant formula using monotone partitions. We investigate some other topics such as infinite divisibility for the additive convolution and deformations of the monotone convolution. We define cumulants for a general convolution to analyze the deformed convolutions.

学術雑誌論文

Accepted Manuscript

Electronic version of an article published as Infinite dimensional analysis, quantum probability and related topics, Vol. 14, No. 03, pp. 465-516 (2011), doi.org/10.1142/S0219025711004444 ©copyright World Scientific Publishing Company https://www.worldscientific.com/worldscinet/idaqp

0219-0257

1793-6306