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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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Submitted on : Thursday, October 25, 2018 - 12:11:22 AM
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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, Oxford University Press (OUP), In press, ⟨10.1093/imrn/rny269⟩. ⟨hal-01608945v3⟩

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