Monotone Cumulant-Moment Formula and Schr\"oder Trees
Octavio Arizmendi, Adrian Celestino
TL;DR
This paper introduces a new formula connecting multivariate monotone cumulants and moments using a Hopf algebra structure on decorated Schr"oder trees, advancing the mathematical understanding of cumulant-moment relations.
Contribution
It develops a novel combinatorial Hopf algebra framework based on Schr"oder trees to express multivariate monotone cumulants in terms of moments.
Findings
Established a formula linking cumulants and moments via Schr"oder trees
Developed a Hopf algebra structure for decorated Schr"oder trees
Enhanced the mathematical tools for studying monotone cumulants
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 Schr\"oder trees.
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Taxonomy
TopicsRandom Matrices and Applications · Graph theory and applications · Complex Network Analysis Techniques