Related papers: The Kummer distribution in free probability, and i…
The empirical probability density function for the conditional distribution of the true value of Poisson distribution parameter on one measurement is constructed by computer experiment. The analysis of the obtained distributions confirms…
Let k be a positive integer and let D_k denote the space of joint distributions for k-tuples of selfadjoint elements in C*-probability space. The paper studies the concept of "subordination distribution of \mu \boxplus \nu with respect to…
We obtain a formula for the density of the free convolution of an arbitrary probability measure on the unit circle of $\mathbb{C}$ with the free multiplicative analogues of the normal distribution on the unit circle. This description relies…
We express classical, free, Boolean and monotone cumulants in terms of each other, using combinatorics of heaps, pyramids, Tutte polynomials and permutations. We completely determine the coefficients of these formulas with the exception of…
This is an introduction to some of the most probabilistic aspects of free probability theory.
Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the product $XY$ is derived. Some basic distributional properties are also derived, including…
In this paper, we will consider the free probabilistic information about compressed random variables in a graph W*-Probability space. Recall the diagonal compressed random variables in a graph W*-probability space. In particular, we can see…
We define a new independence in non-commutative probability, called $\alpha$-freeness, with respect to a triplet of states. This concept unifies several independences in non-commutative probability, in particular, free, monotone,…
We introduce a series of numbers which serve as a generalization of Bernoulli, Euler numbers and binomial coefficients. Their properties are applied to solve a probability problem and suggest a statistical test for independence and…
We construct spaces of quantum increasing sequences, which give quantum families of maps in the sense of Soltan. We then introduce a notion of quantum spreadability for a sequence of noncommutative random variables, by requiring their joint…
In this paper, we study compound bi-free Poisson distributions for {\sl two-faced families of random variables}. We prove a Poisson limit theorem for compound bi-free Poisson distributions. Furthermore, a bi-free infinitely divisible…
The copula representations for conditionally independent random variables and the distribution properties of order statistics of these random variables are studied.
We continue the investigation of noncommutative cumulants. In this paper various characterizations of noncommutative Gaussian random variables are proved.
In this paper additive bi-free convolution is defined for general Borel probability measures, and the limiting distributions for sums of bi-free pairs of selfadjoint commuting random variables in an infinitesimal triangular array are…
We study the distribution of entries of a random permutation matrix under a "randomized basis," i.e., we conjugate the random permutation matrix by an independent random orthogonal matrix drawn from Haar measure. It is shown that under…
It is well known that, under some assumptions, the limit distribution of random block matrices and their partial transposition converges to the distributions of random variables in some noncommutative probability space. Using free…
Conditional independence and Markov properties are powerful tools allowing expression of multidimensional probability distributions by means of low-dimensional ones. As multidimensional possibilistic models have been studied for several…
This paper describes the expected characteristic polynomial of the commutator of randomly rotated matrices, in the context of the finite free probability theory initiated by Marcus, Spielman, and Srivastava. The key technical features are…
We investigate analytical properties of free stable distributions and discover many connections with their classical counterparts. Our main result is an explicit formula for the Mellin transform, which leads to explicit series…
I give a survey about my work on combinatorial and probabilistic aspects of free probability theory. In particular, I present the combinatorial description of freeness in terms of free cumulants and I give some ideas of the main results of…