611 citations · 4.9k across the 114 of their papers we have counts for
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Combinatorial Hopf algebras in noncommutative probabilility
Franz Lehner, Jean-Christophe Novelli, Jean-Yves Thibon
We prove that the generalized moment-cumulant relations introduced in [arXiv:1711.00219] are given by the action of the Eulerian idempotents on the Solomon-Tits algebras, whose dir…
Relations between cumulants in noncommutative probability
Octavio Arizmendi, Takahiro Hasebe, Franz Lehner +1
We express classical, free, Boolean and monotone cumulants in terms of each other, using combinatorics of heaps, pyramids, Tutte polynomials and permutations. We completely determi…
A Noncrossing Basis for Noncommutative Invariants of SL(2,C)
Franz Lehner
Noncommutative invariant theory is a generalization of the classical invariant theory of the action of $SL(2,\IC)$ on binary forms. The dimensions of the spaces of invariant noncom…
Cumulants in Noncommutative Probability Theory III. Creation- and annihilation operators on Fock spaces
Franz Lehner
Fock space constructions give rise to natural exchangeable families and are thus well suited for cumulant calculations. In this paper we develop some general formulas and compute c…
Cumulants in noncommutative probability II. Generalized Gaussian random variables
Franz Lehner
We continue the investigation of noncommutative cumulants. In this paper various characterizations of noncommutative Gaussian random variables are proved.
Cumulants in noncommutative probability I. Noncommutative Exchangeability Systems
Franz Lehner
Cumulants linearize convolution of measures. We use a formula of Good to define noncommutative cumulants in a very general setting.It turns out that the essential property needed i…