Wick polynomials in non-commutative probability: A group-theoretical approach

Wick polynomials and Wick products are studied in the context of non-commutative probability theory. It is shown that free, boolean and conditionally free Wick polynomials can be defined and related through the action of the group of characters over a particular Hopf algebra. These results generalize our previous developments of a Hopf algebraic approach to cumulants and Wick products in classical probability theory.

Keywords

Wick polynomials, monotone cumulants, free cumulants, boolean cumulants, formal power series, combinatorial Hopf algebra, shuffle algebra, group actions

URI

https://oa.tib.eu/renate/handle/123456789/9327
https://doi.org/10.34657/8365

Citation

Ebrahimi-Fard, K., Patras, F., Tapia, N., & Zambotti, L. (2020). Wick polynomials in non-commutative probability: A group-theoretical approach (Vol. 2677). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik. https://doi.org//10.20347/WIAS.PREPRINT.2677

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Mathematik
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