120 citations · 691 across the 56 of their papers we have counts for
62 papers
The Exponential Lie Series and a Chen-Strichartz Formula for Levy Processes
Kurusch Ebrahimi-Fard, Frederic Patras, Anke Wiese
In this paper, we derive a Chen-Strichartz formula for stochastic differential equations driven by Levy processes, that is, we derive a series expansion of the logarithm of the flo…
Effective Action in Free Probability
Kurusch Ebrahimi-Fard, Frederic Patras
Recent works have explored relations between classical and quantum statistical physics on the one hand and Voiculescu's theory of free probability on the other. Motivated by these…
Algebraic structures underlying quantum independences : Theory and Applications
Raphael Chetrite, Frederic Patras
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 more algebr…
Algebraic groups in non-commutative probability theory revisited
Ilya Chevyrev, Kurusch Ebrahimi-Fard, Frédéric Patras
The role of coalgebras as well as algebraic groups in non-commutative probability has long been advocated by the school of von Waldenfels and Schürmann. Another algebraic approach…
Shifted Substitution in Non-Commutative Multivariate Power Series with a View Toward Free Probability
Kurusch Ebrahimi-Fard, Frédéric Patras, Nikolas Tapia +1
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.…
A forest formula for pre-Lie exponentials, Magnus' operator and cumulant-cumulant relations
Adrian Celestino, Frédéric Patras
Forest formulas that generalize Zimmermann's forest formula in quantum field theory have been obtained for the computation of the antipode in the dual of enveloping algebras of pre…