Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 18 (2022), 073, 22 pages      arXiv:2111.02179      https://doi.org/10.3842/SIGMA.2022.073
Contribution to the Special Issue on Non-Commutative Algebra, Probability and Analysis in Action

Monotone Cumulant-Moment Formula and Schröder Trees

Octavio Arizmendi a and Adrian Celestino b
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

Received March 23, 2022, in final form September 25, 2022; Published online October 07, 2022

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.

Key words: noncommutative probability; cumulants; monotone cumulants; moment-cumulant formula; Schröder trees; Hopf algebras.

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