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Article Dans Une Revue International Mathematics Research Notices Année : 2018

Hopf-algebraic deformations of products and Wick polynomials

Résumé

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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Dates et versions

hal-01608945 , version 1 (03-10-2017)
hal-01608945 , version 2 (05-04-2018)
hal-01608945 , version 3 (25-10-2018)

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Kurusch Ebrahimi-Fard, Frédéric Patras, Nikolas Tapia, Lorenzo Zambotti. Hopf-algebraic deformations of products and Wick polynomials. International Mathematics Research Notices, 2018, rny269, pp.1--36. ⟨10.1093/imrn/rny269⟩. ⟨hal-01608945v3⟩
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