Homotopical perspective on statistical quantities
type: Item
instance of: scholarly article
title: Homotopical perspective on statistical quantities
zbMATH Open document ID: 1470.55007
author: Nissim Ranade
published in: Journal of Homotopy and Related Structures
publication date: 2021-05-03T00:00:00Z
review text: Classically, cumulants are functions that measure dependence of random variables. If the random variables are independent then the cumulants are zero. Those notions can be defined in general for linear maps between commutative [\textit{G. C. Drummond-Cole} et al., J. Homotopy Relat. Struct. 10, No. 3, 623--635 (2015; Zbl 1346.55018)] or associative algebras [\textit{F. Lehner}, Math. Z. 248, No. 1, 67--100 (2004; Zbl 1089.46040)] which do not respect the algebraic structure. These cumulants have a close relationship with \(A_\infty\) and \(C_\infty\) morphisms [\textit{J.-L. Loday} and \textit{B. Vallette}, Algebraic operads. Berlin: Springer (2012; Zbl 1260.18001)], which are the classical homotopical tools for analyzing deformations of algebraically compatible linear maps. \par The author studies these two different perspectives to understand how infinity morphisms might help our understanding of cumulants. The main result in this paper is that in the presence of an \(A_\infty\) or \(C_\infty\) morphism, the relevant cumulants are strongly homotopic to zero.
reviewed by: Marek Golasiński
Mathematics Subject Classification ID: 55U35
Mathematics Subject Classification ID: 16E45
Mathematics Subject Classification ID: 18A50
Mathematics Subject Classification ID: 62R30
Mathematics Subject Classification ID: 60A99
zbMATH DE Number: 7342598
zbMATH Keywords: \(A_\infty\) and \(C_\infty\) morphisms
zbMATH Keywords: Boolean cumulants
zbMATH Keywords: cumulants
MaRDI profile type: Publication
full work available at URL: s40062-020-00273-1
OpenAlex ID: W3128473003
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DOI: 10.1007/S40062-020-00273-1
description: scientific article; zbMATH DE number 7342598