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Article

Keywords:
free cumulants; operads; operator-valued cumulants
Summary:
An operadic framework is developed to explain the inversion formula relating moments and cumulants in operator-valued free probability theory.
References:
[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
[2] Drummond-Cole, Gabriel C., Park, Jae-Suk, Terilla, John: Homotopy probability theory I. J. Homotopy Relat. Struct., 10:425–435
[3] Drummond-Cole, Gabriel C., Park, Jae-Suk, Terilla, John: Homotopy probability theory II. J. Homotopy Relat. Struct., 10:623–635
[4] Drummond-Cole, Gabriel C., Terilla, John: Cones in homotopy probability theory. arXiv:1410.5506
[5] Hasebe, Takahiro, Saigo, Hayato: Joint cumulants for natural independence. Elect. Comm. in Probab., 16:491–506
[6] Loday, Jean-Louis, Vallette, Bruno: Algebraic Operads, volume 346 of Grundlehren Math. Wiss. Springer Verlag
[7] Male, Camille: Traffic distributions and independence: permutation invariant random matrices and the three notions of independence. arXiv:1111.4662
[8] Méndez, Miguel A.: Set operads in combinatorics and computer science. Springer Briefs Math. Springer
[9] Muraki, Naofumi: The five independences as quasi-universal products. Infin. Dimens. Anal. Quantum Probab. Relat. Top., 5(1):113–134
[10] Park, Jae-Suk: Homotopy theory of probability spaces I: Classical independence and homotopy Lie algebras. arXiv:1510.08289
[11] Rota, Gian-Carlo, Shen, Jianhong: On the combinatorics of cumulants. J. Combin. Theory. Ser. A, 91:283–304
[12] Speicher, Roland: On universal products. In Free Probability Theory, volume 12 of Fields Inst. Commun., pages 257–266. Amer. Math. Soc
[13] Speicher, Roland: Combinatorial theory of the free product with amalgamation and operator-valued free probability theory. Mem. Amer. Math. Soc., 132(627):88p
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