Shifted substitution in non-commutative multivariate power series with a view toward free probability

K Ebrahimi-Fard, F Patras, N Tapia, L Zambotti - … Integrability and Geometry …, 2023 - emis.de
We study a particular group law on formal power series in non-commuting variables induced
by their interpretation as linear forms on a suitable graded connected word Hopf algebra …

Schr\" oder trees, antipode formulas and non-commutative probability

A Celestino, Y Vargas - arXiv preprint arXiv:2311.07824, 2023 - arxiv.org
We obtain a cancellation-free formula, represented in terms of Schr\" oder trees, for the
antipode in the double tensor Hopf algebra introduced by Ebrahimi-Fard and Patras. We …

Algebraic structures underlying quantum independences: Theory and Applications

R Chetrite, F Patras - Annales Henri Poincaré, 2024 - Springer
The present survey results from the will to reconcile two approaches to quantum
probabilities: one rather physical and coming directly from quantum mechanics, the other …

Schröder trees, antipode formulas and non-commutative probability

A Celestino, Y Vargas - 2023 - graz.elsevierpure.com
We obtain a cancellation-free formula, represented in terms of Schröder trees, for the
antipode in the double tensor Hopf algebra introduced by Ebrahimi-Fard and Patras. We …

Cumulants in Non-commutative: Probability via Hopf Algebras

AJC Rodriguez - 2022 - ntnuopen.ntnu.no
The notion of cumulants plays a significant role in the combinatorial study of
noncommutative probability theory. In this thesis, we study several problems associated with …

[引用][C] Informatique mathématique: une photographie en 2022

O Bournez, R Chetrite, N Fijalkow, E Formenti… - 2022 - CNRS Edition