Related papers: Relations between convolutions and transforms in o…
Free probability theory was created by Dan Voiculescu around 1985, motivated by his efforts to understand special classes of von Neumann algebras. His discovery in 1991 that also random matrices satisfy asymptotically the freeness relation…
Extensive studies of Boolean functions are carried in many fields. The Mobius transform is often involved for these studies. In particular, it plays a central role in coincident functions, the class of Boolean functions invariant by this…
This work proposes algorithms for computing additive and multiplicative free convolutions of two given measures. We consider measures with compact support whose free convolution results in a measure with a density function that exhibits a…
The $\mathcal{A}$-tracial algebras are algebras endowed with multi-linear forms, compatible with the product, and indexed by partitions. Using the notion of $\mathcal{A}$-cumulants, we define and study the $\mathcal{A}$-freeness property…
We extend an algebra of Mantaci and Reutenauer, acting on the free associative algebra, to a vector space of operators acting on all graded connected Hopf algebras. These operators are convolution products of certain involutions, which we…
Belinschi and Nica introduced a composition semigroup on the set of probability measures. Using this semigroup, they introduced a free divisibility indicator, from which one can know whether a probability measure is freely infinitely…
In this article, we introduce the notion of free subexponentiality, which extends the notion of subexponentiality in the classical probability setup to the noncommutative probability spaces under freeness. We show that distributions with…
In the process of developing the theory of free probability and free entropy, Voiculescu introduced in 1991 a random matrix model for a free semicircular system. Since then, random matrices have played a key role in von Neumann algebra…
In this paper, we study a class of convolution operators on the space of distributions that enlarge the well-studied class of passive operators. In this larger class, we are able to associate, to each operator, a holomorphic function in the…
Voiculescu's random matrix model for freeness is extended to the non-Gaussian case and also the case of constant block diagonal matrices. Thus we are able to investigate free products of free group factors with matrix algebras and with the…
We propose periodic Macdonald processes as a $(q,t)$-deformation of periodic Schur processes and a periodic analogue of Macdonald processes. It is known that, in the theory of stochastic processes related to a family of symmetric functions,…
In a central lemma we characterize "generating functions" of certain functors on the category of algebraic non-commutative probability spaces. Special families of such generating functions correspond to "unital, associative universal…
A map is given showing that convolutions of independent random variables over a finite group and matrix multiplications of doubly stochastic matrices are homomorphic. As an application, a short proof is given to the theorem that the…
This paper is devoted to studying a system of coupled nonlinear first order history-dependent evolution inclusions in the framework of evolution triples of spaces. The multivalued terms are of the Clarke subgradient or of the convex…
An ordinal view of independence is studied in the framework of possibility theory. We investigate three possible definitions of dependence, of increasing strength. One of them is the counterpart to the multiplication law in probability…
Using the technique developed in approximation theory, we construct examples of exponential families of infinitely divisible laws which can be viewed as deformations of the normal, gamma, and Poisson exponential families. Replacing the…
The paper gives an operator algebras model for the conditional monotone independence, introduced by T. Hasebe. The construction is used to prove an embedding result for the N. Muraki's monotone product of C*-algebras. Also, the formulas…
We define and study a relative free entropy quantity, analogous in its properties to Voiculescu's relative free entropy Chi^*(...:B). Our definition uses matricial microstates, unlike his definition, which involves non-commutative Hilbert…
Measuring a strength of dependence of random variables is an important problem in statistical practice. In this paper, we propose a new function valued measure of dependence of two random variables. It allows one to study and visualize…
Valuation networks have been proposed as graphical representations of valuation-based systems (VBSs). The VBS framework is able to capture many uncertainty calculi including probability theory, Dempster-Shafer's belief-function theory,…