Heavy tails are often found in practice, and yet they are an Achilles heel of a variety of
mainstream random probability measures such as the Dirichlet process (DP). The first …

In a fundamental lemma we characterize “generating functions” of certain functors on the
category of algebraic non-commutative probability spaces. Special families of such …

We attack the classification problem of multi-faced independences, the first non-trivial
example being Voiculescu's bi-freeness. While the present paper does not achieve a …

We determine a set of necessary conditions on a partition-indexed family of complex
numbers to be the``highest coefficients''of a positive and symmetric multi-faced universal …

We extend the Schoenberg correspondence for universal independences by Sch\" urmann
and Vo {\ss} to the multivariate setting of Manzel and Sch\" urmann, covering, eg …

We generalize Franz'independence in tensor categories with inclusions from two morphisms
(which represent generalized random variables) to arbitrary ordered families of morphisms …

We study states on the universal noncommutative⁎-algebra generated by the coefficients of
a unitary matrix, or equivalently states on the unitary dual group. Its structure of dual group in …

Universal products provide an axiomatic framework to study noncommutative
independences general enough to include, besides the well known" single-faced" case (ie …

Here we extend the algebro-geometric approach to free probability, started in~\cite {FMcK4,
F14}, to general (non)-commutative probability theories. We show that any universal …

A simplification of the proof of the classification theorem for natural notions of stochastic
independence is given. This simplification is made possible after adding the positivity …