WIAS Preprint No. 2677, (2020)
Wick polynomials in non-commutative probability: A group-theoretical approach
Authors
- Ebrahimi-Fard, Kurusch
- Patras, Frédéric
- Tapia, Nikolas
ORCID: 0000-0003-0018-2492 - Zambotti, Lorenzo
2010 Mathematics Subject Classification
- 16T05 16T10 16T30
Keywords
- Wick polynomials, monotone cumulants, free cumulants, boolean cumulants, formal power series, combinatorial Hopf algebra, shuffle algebra, group actions
DOI
Abstract
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.
Appeared in
- Comput. Fluids, (2021), published online on 25.08.2021, DOI 10.4153/S0008414X21000407 .
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