4 papers
Combinatorics of cyclic-conditional freeness
Octavio Arizmendi, Guillaume Cébron, Nicolas Gilliers
This work investigates the combinatorial structures underlying cyclic conditional freeness and introduces cumulants that serve to linearize the cyclic conditional additive convolut…
Bigraph independence : a mixture of the five natural independences
Nicolas Gilliers, David Jekel
We introduce a notion of non-commutative joint independence for multiple algebras in a non-commutative probability space. The pairwise relationships between these algebras are enco…
Jacobson identities for post-Lie algebras in positive characteristic
Quentin Ehret, Nicolas Gilliers
Let be a prime number. Given a restricted Lie algebra over a field of characteristic and a post-Lie operation over it, we prove the Jacobson identities for a -structure…
Post-Hopf algebra in non-commutative probability theory
Nicolas Gilliers
We study -operators and post-Lie products over the same Lie algebra compatible in a certain sense. We prove that the group product corresponding to the formal integrat…