相关论文: Cumulants in noncommutative probability I. Noncomm…
Non-commutative propositions are characteristic of both quantum and non-quantum (sociological, biological, psychological) situations. In a Hilbert space model states, understood as correlations between all the possible propositions, are…
For exchangeable data, mixture models are an extremely useful tool for density estimation due to their attractive balance between smoothness and flexibility. When additional covariate information is present, mixture models can be extended…
We establish explicit, universal, and distribution-free bounds for the $n$-th cumulant, $\kappa_n(X)$, of a scalar random variable, controlled solely by an $n$-th order absolute moment functional $M_n(X)$. The bounds take the form…
In plethora of physical situations one can distinguish a mediator -- a system that couples other, non-interacting systems. Often the mediator itself is not directly accessible to experimentation, yet it is interesting and sometimes crucial…
A fundamental aspect of the quantum-to-classical limit is the transition from a non-commutative algebra of observables to commutative one. However, this transition is not possible if we only consider unitary evolutions. One way to describe…
We introduce a category of noncommutative bundles. To establish geometry in this category we construct suitable noncommutative differential calculi on these bundles and study their basic properties. Furthermore we define the notion of a…
We review the main features of the Weyl-Wigner formulation of noncommutative quantum mechanics. In particular, we present a $\star$-product and a Moyal bracket suitable for this theory as well as the concept of noncommutative Wigner…
We propose new algorithms for generating $k$-statistics, multivariate $k$-statistics, polykays and multivariate polykays. The resulting computational times are very fast compared with procedures existing in the literature. Such speeding up…
We study the entanglement entropy and particle number cumulants for a system of disordered noninteracting fermions in $d$ dimensions. We show, both analytically and numerically, that for a weak disorder the entanglement entropy and the…
Conditional copulas are flexible statistical tools that couple joint conditional and marginal conditional distributions. In a linear regression setting with more than one covariate and two dependent outcomes, we propose the use of additive…
Sequences of actions do not commute.. For example, the tick of a clock and the measurement of a position do not commute with one another, since the position will have moved to the next position after the tick. We adopt non-commutative…
We formulate a Born rule for families of quantum systems parametrized by a noncommutative space of control parameters. The resulting formalism may be viewed as a generalization of quantum mechanics where overlaps take values in a…
This paper presents an introduction to the stochastic concepts of \emph{coupling} and \emph{copula}. Coupling means the construction of a joint distribution of two or more random variables that need not be defined on one and the same…
First, we present a concise glossary of formulas for composition of standard, cumulant, factorial, and factorial cumulant moments in superposition (compound) models, where final particles are created via independent emission from a…
A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher…
This paper extends the classical theory of joinings of measurable dynamical systems to the noncommutative setting from several interconnected points of view. Among these is a particularly fruitful identification of joinings with equivariant…
We study the dynamics of a quantum system in which an intermediate property $m$ is measured in between initial and final measurements of two different non-commuting properties $a$ and $b$. Since this intermediate measurement must involve an…
Considering commutator monomials of the non-commutative associative variables $X_1,\ldots,X_n$; we determine the maximal possible number of alternating associative monomials in their noncommutative polynomial expansions. This is achieved by…
A quantum decaying system can reveal its nonclassical behavior by being noninvasively measured. Correlations of weak measurements in the noninvasive limit violate the classical bound for a universal class of systems. The violation is…
We show that the strength of non-commutativity could play a role in determining the boundary condition of a physical problem. As a toy model we consider the inverse square problem in non-commutative space. The scale invariance of the system…