Related papers: Free-Boolean independence with amalgamation
In this paper, we consider the relation between the group freeness and the amalgamated freeness of crossed product algebras.
The partial copula provides a method for describing the dependence between two random variables $X$ and $Y$ conditional on a third random vector $Z$ in terms of nonparametric residuals $U_1$ and $U_2$. This paper develops a nonparametric…
Let A be a commutative unital C*-algebra and let S denote its Gelfand spectrum. We give some necessary and sufficient conditions for a nondegenerate representation of A to be unitarily equivalent to a multiplicative representation on a…
Let A be a unital $C^*$-algebra, given together with a specified state $\phi:A \to C$. Consider two selfadjoint elements a,b of A, which are free with respect to $\phi$ (in the sense of the free probability theory of Voiculescu). Let us…
We investigate the implications of free probability for random matrices. From rules for calculating all possible joint moments of two free random matrices, we develop a notion of partial freeness which is quantified by the breakdown of…
We propose a general formalism to compute exact correlation functions for Cardy's boundary states. Using the free-field construction of boundary states and applying the Coulomb-gas technique, it is shown that charge-neutrality conditions…
A model-free measure of coupling between dynamical variables is built from time series embedding principle. The approach described does not require a mathematical form for the dynamics to be assumed. The approach also does not require…
We study dynamical tunneling in a near-integrable Hamiltonian with three degrees of freedom. The model Hamiltonian does not have any discrete symmetry. Despite this lack of symmetry we show that the mixing of near-degenerate quantum states…
Recognizing, quantifying and visualizing associations between two variables is increasingly important. This paper investigates how a new function-valued measure of dependence, the quantile dependence function, can be used to construct tests…
Given a functor $F: \mathcal{C} \to \mathcal{D}$ and a model-theoretic independence relation on $\mathcal{D}$, we can lift that independence relation along $F$ to $\mathcal{C}$ by declaring a commuting square in $\mathcal{C}$ to be…
In this paper, we introduce quotients of \'etale groupoids. Using the notion of quotients, we describe the abelianizations of groupoid C*-algebras. As another application, we obtain a simple proof that effectiveness of an \'etale groupoid…
In a recent paper we have suggested that a formulation of quantum mechanics should exist, which does not require the concept of time, and that the appropriate mathematical language for such a formulation is noncommutative differential…
The generalization of the concept of interaction-free evolutions (IFE) [A. Napoli, {\it et al.}, Phys. Rev. A {\bf 89}, 062104 (2014)] to the case of time-dependent Hamiltonians is discussed. It turns out that the time-dependent case allows…
I show that in a standard process algebra extended with time-outs one can correctly model mutual exclusion in such a way that starvation-freedom holds without assuming fairness or justness, even when one makes the problem more challenging…
The modulation and engineering of the free-electron wave function bring new ingredients to the electron-matter interaction. We study the dynamics of a free-electron passing by a two-level system fully quantum mechanically and emphasize the…
We presents an independence relation on sets, one can define dimension by it, assuming that we have an abstract elementary class with a forking notion that satisfies the axioms of a good frame minus stability.
Two known results on the relationship between conditional and unconditional independence are obtained as a consequence of the main result of this paper, a theorem that uses independence of Markov kernels to obtain a minimal condition which…
We reformulate base point free theorems. Our formulation is flexible and has some important applications. One of the main purposes of this paper is to prove a generalization of the base point free theorem in Fukuda's paper: On numerically…
We investigate the algebra and geometry of the independence conditions on discrete random variables in which we fix some random variables and study the complete independence of some subcollections. We interpret such independence conditions…
Conditional independence in a multivariate normal (or Gaussian) distribution is characterized by the vanishing of subdeterminants of the distribution's covariance matrix. Gaussian conditional independence models thus correspond to algebraic…