Related papers: A three-state independence in non-commutative prob…
$C_\infty$ Algebras and their morphisms are a framework in which one can study algebras and their maps that are not commutaive-associative but are homotopic to being that. In statistics cumulants measure the independence of random…
Following our previous work on copula-based nonsymmetric bivariate dependence measures, we propose a new set of conditions on nonsymmetric multivariate dependence measures which characterize both independence and complete dependence of one…
Bergsma (2006) proposed a covariance $\kappa$(X,Y) between random variables X and Y. He derived their asymptotic distributions under the null hypothesis of independence between X and Y. The non-null (dependent) case does not seem to have…
We describe a novel way to represent the probability distribution of a random binary string as a mixture having a maximally weighted component associated with independent (though not necessarily identically distributed) Bernoulli…
We study $N$-ary non-commutative notions of independence, which are given by trees and which generalize free, Boolean, and monotone independence. For every rooted subtree $\mathcal{T}$ of the $N$-regular tree, we define the…
Characterization problems in free probability are studied here. Using subordination of free additive and free multiplicative convolutions we generalize some known characterizations in free probability to random variables with unbounded…
In this article, we propose a new method for the fundamental task of testing for dependence between two groups of variables. The response densities under the null hypothesis of independence and the alternative hypothesis of dependence are…
We introduce a new kind of free independence, called real infinitesimal freeness. We show that independent orthogonally invariant with infinitesimal laws are asymptotically real infinitesimally free. We introduce new cumulants, called real…
We introduce the concept of mutual independence -- correlations shared between distant parties which are independent of the environment. This notion is more general than the standard idea of a secret key -- it is a fully quantum and more…
For triples of probability measures, pure quantum states and mixed quantum states we obtain the exact constraints on the fidelities of pairs in the sequence. We show that it is impossible to decide between a quantum model, either pure or…
We consider two extensions of free probability that have been studied in the research literature, and are based on the notions of c-freeness and respectively of infinitesimal freeness for noncommutative random variables. In a 2012 paper,…
Given observations from a stationary time series, permutation tests allow one to construct exactly level $\alpha$ tests under the null hypothesis of an i.i.d. (or, more generally, exchangeable) distribution. On the other hand, when the null…
We prove general de Finetti type theorems for classical and free independence. The de Finetti type theorems work for all non-easy quantum groups, which generalize a recent work of Banica, Curran and Speicher. We determine maximal…
In an independence model, the triplets that represent conditional independences between singletons are called elementary. It is known that the elementary triplets represent the independence model unambiguously under some conditions. In this…
In this work we describe a protocol by which two of three parties generate two bipartite entangled state among themselves without involving third party, from a non maximal W state or W - type state…
Motivated by the recent work on asymptotic independence relations for random matrices with non-commutative entries, we investigate the limit distribution and independence relations for large matrices with identically distributed and Boolean…
We study distributions of polynomials in conditionally free (c-free) random variables, a notion of independence for two-state noncommutative probability spaces introduced by Bozejko, Leinert and Speicher. To this end we establish recursive…
We introduce and study the notion of k-divisible elements in a non-commutative probability space. A k-divisible element is a (non-commutative) random variable whose n-th moment vanishes whenever n is not a multiple of k. First, we consider…
As in the cases of freeness and monotonic independence, the notion of conditional freeness is meaningful when complex-valued states are replaced by positive conditional expectations. In this framework, the paper presents several positivity…
We introduce the coverage correlation coefficient, a novel nonparametric measure of statistical association designed to quantifies the extent to which two random variables have a joint distribution concentrated on a singular subset with…