An operadic approach to operator-valued free cumulants
Gabriel C. Drummond-Cole
TL;DR
This paper introduces an operadic framework to clarify the relationship between moments and cumulants in operator-valued free probability, providing a new mathematical perspective on these concepts.
Contribution
It develops an operadic approach that offers a novel and structured way to understand the inversion formula in operator-valued free probability.
Findings
Operadic structures elucidate moment-cumulant relations.
The framework simplifies inversion formulas.
Provides new tools for operator-valued free probability analysis.
Abstract
An operadic framework is developed to explain the inversion formula relating moments and cumulants in operator-valued free probability theory.
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Taxonomy
TopicsRandom Matrices and Applications · Quantum Mechanics and Applications · Advanced Algebra and Logic