Wick polynomials in non-commutative probability: A group-theoretical approach
- Ebrahimi-Fard, Kurusch
- Patras, Frédéric
- Tapia, Nikolas
- Zambotti, Lorenzo
2010 Mathematics Subject Classification
- 16T05 16T10 16T30
- Wick polynomials, monotone cumulants, free cumulants, boolean cumulants, formal power series, combinatorial Hopf algebra, shuffle algebra, group actions
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.
- Comput. Fluids, (2021), published online on 25.08.2021, DOI 10.4153/S0008414X21000407 .