| Title:
|
An operadic approach to operator-valued free cumulants (English) |
| Author:
|
Drummond-Cole, Gabriel C. |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
2 |
| Issue:
|
1 |
| Year:
|
2018 |
| Pages:
|
42-56 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
An operadic framework is developed to explain the inversion formula relating moments and cumulants in operator-valued free probability theory. (English) |
| Keyword:
|
free cumulants |
| Keyword:
|
operads |
| Keyword:
|
operator-valued cumulants |
| MSC:
|
18D50 |
| MSC:
|
46L54 |
| idZBL:
|
Zbl 1417.46045 |
| idMR:
|
MR3917426 |
| DOI:
|
10.21136/HS.2018.03 |
| . |
| Date available:
|
2026-03-10T15:17:22Z |
| Last updated:
|
2026-03-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153402 |
| . |
| Reference:
|
[1] Drummond-Cole, Gabriel C.: A non-crossing word cooperad for free homotopy probability theory..In 2016 MATRIX Annals, volume 1 of MATRIX Book Series, pages 77–99. Springer |
| Reference:
|
[2] Drummond-Cole, Gabriel C., Park, Jae-Suk, Terilla, John: Homotopy probability theory I..J. Homotopy Relat. Struct., 10:425–435 |
| Reference:
|
[3] Drummond-Cole, Gabriel C., Park, Jae-Suk, Terilla, John: Homotopy probability theory II..J. Homotopy Relat. Struct., 10:623–635 |
| Reference:
|
[4] Drummond-Cole, Gabriel C., Terilla, John: Cones in homotopy probability theory..arXiv:1410.5506 |
| Reference:
|
[5] Hasebe, Takahiro, Saigo, Hayato: Joint cumulants for natural independence..Elect. Comm. in Probab., 16:491–506 |
| Reference:
|
[6] Loday, Jean-Louis, Vallette, Bruno: Algebraic Operads, volume 346 of Grundlehren Math. Wiss..Springer Verlag |
| Reference:
|
[7] Male, Camille: Traffic distributions and independence: permutation invariant random matrices and the three notions of independence..arXiv:1111.4662 |
| Reference:
|
[8] Méndez, Miguel A.: Set operads in combinatorics and computer science..Springer Briefs Math. Springer |
| Reference:
|
[9] Muraki, Naofumi: The five independences as quasi-universal products..Infin. Dimens. Anal. Quantum Probab. Relat. Top., 5(1):113–134 |
| Reference:
|
[10] Park, Jae-Suk: Homotopy theory of probability spaces I: Classical independence and homotopy Lie algebras..arXiv:1510.08289 |
| Reference:
|
[11] Rota, Gian-Carlo, Shen, Jianhong: On the combinatorics of cumulants..J. Combin. Theory. Ser. A, 91:283–304 |
| Reference:
|
[12] Speicher, Roland: On universal products..In Free Probability Theory, volume 12 of Fields Inst. Commun., pages 257–266. Amer. Math. Soc |
| Reference:
|
[13] Speicher, Roland: Combinatorial theory of the free product with amalgamation and operator-valued free probability theory..Mem. Amer. Math. Soc., 132(627):88p |
| . |
