611 citations · 4.9k across the 114 of their papers we have counts for
116 papers
Cyclic independence: Boolean and monotone
Octavio Arizmendi, Takahiro Hasebe, Franz Lehner
The present paper introduces a modified version of cyclic-monotone independence which originally arose in the context of random matrices, and also introduces its natural analogy ca…
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…
The Free Tangent Law
Wiktor Ejsmont, Franz Lehner
Nevanlinna-Herglotz functions play a fundamental role for the study of infinitely divisible distributions in free probability. In the present paper we study the role of the tangent…
The Trace Method for Cotangent Sums
Wiktor Ejsmont, Franz Lehner
This paper presents a combinatorial study of sums of integer powers of the cotangent which is a popular theme in classical calculus. Our main tool the realization of cotangent valu…
Sums of Commutators in Free Probability
Wiktor Ejsmont, Franz Lehner
We study the linear span of commutators of free random variables and show that these are the only quadratic forms which satisfy the following equivalent properties: * preservation…
Boolean Cumulants and Subordination in Free Probability
Franz Lehner, Kamil Szpojankowski
We study subordination of free convolutions. We prove that for free random variables and a Borel function the conditional expectation $E_φ\left[ (z-X-f(X)Yf^*(X))^{-1}| X…