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Symmetry, Integrability and Geometry: Methods and Applications, 2022, Volume 18, 073, 22 pp.
DOI: https://doi.org/10.3842/SIGMA.2022.073 (Mi sigma1869) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Monotone Cumulant-Moment Formula and Schröder Trees

Octavio Arizmendia, Adrian Celestinob

a Centro de Investigación en Matemáticas, Calle Jalisco SN, Guanajuato, Mexico
b Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway
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DOI: https://doi.org/10.3842/SIGMA.2022.073
Abstract: We prove a formula to express multivariate monotone cumulants of random variables in terms of their moments by using a Hopf algebra of decorated Schröder trees.
Keywords: noncommutative probability, cumulants, monotone cumulants, moment-cumulant formula, Schröder trees, Hopf algebras.
Funding agency Grant number
CONACYT - Consejo Nacional de Ciencia y Tecnología CB-2017-2018-A1-S-97
Deutsche Forschungsgemeinschaft SFB-TRR 195
Trond Mohn Foundation
Tromsø Research Foundation
Octavio Arizmendi received financial support by CONACYT Grant CB-2017-2018-A1-S-9764 “Matrices Aleatorias y Probabilidad No Conmutativa” and by the SFB-TRR 195 “Symbolic Tools in Mathematics and their Application” of the German Research Foundation (DFG). Adrian Celestino was partially supported by the project Pure Mathematics in Norway, funded by Trond Mohn Foundation and Tromsø Research Foundation.
Received: March 23, 2022; in final form September 25, 2022; Published online October 7, 2022
Bibliographic databases:
Document Type: Article
MSC: 05E99, 16T05, 17A30, 46L53
Language: English
Citation: Octavio Arizmendi, Adrian Celestino, “Monotone Cumulant-Moment Formula and Schröder Trees”, SIGMA, 18 (2022), 073, 22 pp.
Citation in format AMSBIB
\Bibitem{AriCel22}
\by Octavio~Arizmendi, Adrian~Celestino
\paper Monotone Cumulant-Moment Formula and Schr\"oder Trees
\jour SIGMA
\yr 2022
\vol 18
\papernumber 073
\totalpages 22
\mathnet{http://mi.mathnet.ru/sigma1869}
\crossref{https://doi.org/10.3842/SIGMA.2022.073}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4492885}
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    • This publication is cited in the following 1 articles:
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    		Symmetry, Integrability and Geometry: Methods and Applications
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