Hopf-algebraic Deformations of Products and Wick Polynomials-Reference-Cited by-同舟云学术

Hopf-algebraic Deformations of Products and Wick Polynomials

Published:2018-12-06 Issue:24 Volume:2020 Page:10064-10099
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Ebrahimi-Fard Kurusch¹,Patras Frédéric²,Tapia Nikolas³⁴^ORCID,Zambotti Lorenzo⁴^ORCID

Affiliation:

1. Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), 7491 Trondheim, Norway. On leave from UHA, Mulhouse, France

2. Université Côte d’Azur, National Center for Scientific Research, UMR 7351, Parc Valrose, 06108 Nice Cedex 02, France

3. Departamento de Ingeniería Matemática, Universidad de Chile, Santiago, Chile

4. Laboratoire de Probabilités, Statistique et Modélisation, UMR 8001, Sorbonne Université, Paris, France

Abstract

Abstract We present an approach to cumulant–moment relations and Wick polynomials based on extensive use of convolution products of linear functionals on a coalgebra. This 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 of all orders. We also generalize the notion of deformed product in order to discuss how these ideas appear in the recent theory of regularity structures.

Funder

Combinatoire Algébrique, Résurgence, Moules et Applications

Comisión Nacional de Investigación Científica y Tecnológica

Programa Iniciativa Científica Milenio

Agence Nationale de la Recherche

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2020/24/10064/34949035/rny269.pdf

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