Name
Abstract | ||
|---|---|---|
Relations between moments and cumulants play a central role in both classical and non-commutative probability theory. The latter allows for several distinct families of cumulants corresponding to different types of independences: free, Boolean and monotone. Relations among those cumulants have been studied recently. In this work, we focus on the problem of expressing with a closed formula multivariate monotone cumulants in terms of free and Boolean cumulants. In the process, we introduce various constructions and statistics on non-crossing partitions. Our approach is based on a pre-Lie algebra structure on cumulant functionals. Relations among cumulants are described in terms of the pre-Lie Magnus expansion combined with results on the continuous Baker–Campbell–Hausdorff formula due to A. Murua. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.1007/s10208-021-09512-0 | Foundations of Computational Mathematics |
Keywords | DocType | Volume |
Monotone cumulants, Free cumulants, Boolean cumulants, Irreducible non-crossing partitions, Quasi-monotone partitions, Pre-Lie algebra, Magnus expansion, Rooted trees, 46L53, 46L54, 16T30, 17A30 | Journal | 22 |
Issue | ISSN | Citations |
3 | 1615-3375 | 0 |
PageRank | References | Authors |
0.34 | 5 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Celestino A. | 1 | 0 | 0.34 |
| Ebrahimi-Fard K. | 2 | 0 | 0.34 |
| Patras F. | 3 | 0 | 0.34 |
| Anaya D. Perales | 4 | 0 | 0.34 |