Monotone Cumulant-Moment Formula and Schröder Trees

Arizmendi, Octavio; Celestino, Adrian

doi:10.3842/sigma.2022.073

SIGMA

2022

DOI: 10.3842/sigma.2022.073

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Monotone Cumulant-Moment Formula and Schröder Trees

Octavio Arizmendi¹,

Adrian Celestino²

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.

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2024

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Effective Action in Free Probability

Patras,

Ebrahimi-Fard

2024

Markov Processes and Related Fields

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Recent works have explored relations between classical and quantum statistical physics on the one hand and Voiculescu's theory of free probability on the other. Motivated by these results, the present work focuses on the notion of effective action, which is closely related to the large deviation rate function in classical probability and one-particle irreducible correlation functions in quantum field theories. The central aim is to understand how it can be defined and studied in free probability. In this respect, we introduce a suitable diagrammatic formalism.

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Effective Action in Free Probability

Patras,

Ebrahimi-Fard

2024

Markov Processes and Related Fields

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

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Monotone Cumulant-Moment Formula and Schröder Trees

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.

Cited by 1 publication

References 20 publications

Effective Action in Free Probability

Effective Action in Free Probability

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