Geodesic
Wick polynomials in noncommutative probability: a group-theoretical approach
Canadian journal of mathematics, Tome 74 (2022) no. 6, pp. 1673-1699

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DOI

Wick polynomials and Wick products are studied in the context of noncommutative 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.
DOI : 10.4153/S0008414X21000407
Mots-clés : Wick polynomials, monotone cumulants, free cumulants, Boolean cumulants, formal power series, combinatorial Hopf algebra, shuffle algebra, group actions 
Ebrahimi-Fard, Kurusch; Patras, Frédéric; Tapia, Nikolas; Zambotti, Lorenzo. Wick polynomials in noncommutative probability: a group-theoretical approach. Canadian journal of mathematics, Tome 74 (2022) no. 6, pp. 1673-1699. doi: 10.4153/S0008414X21000407
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     title = {Wick polynomials in noncommutative probability: a group-theoretical approach},
     journal = {Canadian journal of mathematics},
     pages = {1673--1699},
     year = {2022},
     volume = {74},
     number = {6},
     doi = {10.4153/S0008414X21000407},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X21000407/}
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