2 citations · 3 across the 11 of their papers we have counts for
12 papers
Brownian motion on the complex general group and the non-compact Jacobi process
Martin Auer, Nizar Demni, Nicolas Gilliers
In this paper, we introduce and study a new non Hermitian matrix-valued process built from truncations of Brownian motion on complex positive-definite matrices and of its inverse.…
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…
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…
Asymptotic cyclic-conditional freeness of random matrices
Guillaume Cébron, Nicolas Gilliers
Voiculescu's freeness emerges in computing the asymptotic of spectra of polynomials on random matrices with eigenspaces in generic positions: they are randomly rotated…
Shuffle Algebras and Non-Commutative Probability for Pairs of Faces
Joscha Diehl, Malte Gerhold, Nicolas Gilliers
One can build an operatorial model for freeness by considering either the right-handed or the left-handed representation of algebras of operators acting on the free product of the…
On the twisted factorization of the -transform
Kurusch Ebrahimi-Fard, Nicolas Gilliers
The amalgamated -transform of a non-commutative distribution was introduced by K.~Dykema. It provides a fundamental tool for computing distributions of random variables in Voicu…
On the Signature of a Path in an Operator Algebra
Carlo Bellingeri, Nicolas Gilliers
We introduce a class of operators associated with the signature of a smooth path with values in a algebra . These operators serve as the basis of Taylo…
A shuffle algebra point of view on operator-valued probability theory
Nicolas Gilliers
We extend the shuffle algebra perspective on scalar-valued non-commutative probability theory to the operator-valued case. Given an operator-valued probability space with an algebr…
Matricial approximations of higher dimensional master fields
Nicolas Gilliers
We study matricial approximations of master fields we constructed in a previous work. These approximations (in non-commutative distribution) are obtained by extracting blocks of a…
Quantum Holonomy Fields
Nicolas Gilliers
We investigate lattice and continuous quantum gauge theories on the Euclidean plane with a structure group that is replaced by a -algebra; non-commutative analogues of groups an…