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Conditionally monotone independence I: Independence, additive convolutions and related convolutions
| Title: | Conditionally monotone independence I: Independence, additive convolutions and related convolutions |
| Authors: | Hasebe, Takahiro Browse this author →KAKEN DB |
| Keywords: | Conditionally free independence | | monotone independence | | Boolean independence | | free independence | | cumulants |
| Issue Date: | Sep-2011 |
| Journal Title: | Infinite Dimensional Analysis, Quantum Probability and Related Topics |
| Volume: | 14 |
| Issue: | 03 |
| Start Page: | 465 |
| End Page: | 516 |
| Publisher DOI: | 10.1142/S0219025711004444 |
| Abstract: | 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. |
| Rights: | 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 |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/76011 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 長谷部 高広
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