Hopf-algebraic deformations of products and Wick polynomials

Abstract : We present a different approach to classical definitions and results on cumulant-moment relations and Wick polynomials, which is based on extensive use of convolution products of linear functionals on a coalgebra. It allows, in particular, to understand the construction of Wick polynomials as the result of a Hopf algebra deformation under the action of linear automorphisms induced by multivariate moments associated to an arbitrary family of random variables with moments at all orders.
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Pré-publication, Document de travail
Revised and substantially extended version; change of title. 28 pages. 2018
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Contributeur : Nikolas Tapia <>
Soumis le : jeudi 5 avril 2018 - 06:17:54
Dernière modification le : lundi 30 avril 2018 - 13:46:01

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  • HAL Id : hal-01608945, version 2
  • ARXIV : 1710.00735

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Kurusch Ebrahimi-Fard, Frédéric Patras, Nikolas Tapia, Lorenzo Zambotti. Hopf-algebraic deformations of products and Wick polynomials. Revised and substantially extended version; change of title. 28 pages. 2018. 〈hal-01608945v2〉

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