相关论文: Cumulants in noncommutative probability I. Noncomm…
A defining feature of non-stationary systems is the time dependence of their statistical parameters. Measured time series may exhibit Gaussian statistics on short time horizons, due to the central limit theorem. The sample statistics for…
Continuous variable entanglement is a manifestation of nonclassicality of quantum states. In this paper we attempt to analyze whether and under which conditions nonclassicality can be used as an entanglement criterion. We adopt the…
Recently it has been shown that cumulants significantly simplify the analysis of multipartite weak measurements. Here we consider the mathematical structure that underlies this, and find that it can be formulated in terms of what we call…
The high-order cumulants and factorial cumulants of conserved charges are suggested to study the critical dynamics in heavy ion collisions. In this paper, using parametric representation of the 3-dimensional Ising model, the sign…
We reconcile for the first time the strict mathematical formalism of multivariate cumulants with the usage of cumulants in anisotropic flow analyses in high-energy nuclear collisions. This reconciliation yields to the next generation of…
Two examples of the situation when the classical observables should be described by a noncommutative probability space are investigated. Possible experimental approach to find quantum-like correlations for classical disordered systems is…
Deformation quantization is a powerful tool to quantize some classical systems especially in noncommutative space. In this work we first show that for a class of special Hamiltonian one can easily find relevant time evolution functions and…
The cumulants of thermal variables are of general interest in physics due to their extensivity and their correspondence with susceptibilities. They become especially significant near critical points of phase transitions where they diverge…
Cumulants and moments are closely related to the basic mathematics of continuous and discrete selection (respectively). These relationships generalize Fisher's fundamental theorem of natural selection and also make clear some of its…
The entanglement produced by a bilinear Hamiltonian in continuous variables has been thoroughly studied and widely used. In contrast, the physics of entanglement resulting from nonlinear interaction described by partially degenerate…
Composite system is studied in noncommutative phase space with preserved rotational symmetry. We find conditions on the parameters of noncommutativity on which commutation relations for coordinates and momenta of the center-of-mass of…
We generalize the classical probability frame by adopting a wider family of random variables that includes nondeterministic ones. The frame that emerges is known to host a ''classical'' extension of quantum mechanics. We discuss the notion…
In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the…
Shape dependence of higher order correlations introduces complication in direct determination of these quantities. For this reason theoretical and observational progress has been restricted in calculating one point distribution functions…
The covariance between real finite variance random variables can be expressed as the commutator of taking expectations and multiplying, both viewed as operators extended to act jointly on pairs of functions. The efficient influence curve of…
The independent component model is a latent variable model where the components of the observed random vector are linear combinations of latent independent variables. The aim is to find an estimate for a transformation matrix back to…
In complex systems, crucial parameters are often subject to unpredictable changes in time. Climate, biological evolution and networks provide numerous examples for such non-stationarities. In many cases, improved statistical models are…
We argue that there should exist a "noncommutative Fourier transform" which should identify functions of noncommutative variables (say, of matrices of indeterminate size) and ordinary functions or measures on the space of paths. Some…
A method for computing the mixed moments of (not necessarily commutative) random vectors from the first order moments, the $q$-commutators between the annihilation and creation operators, and the $q$-commutators between the annihilation and…
A transfer is a group homomorphism from a finite group to an abelian quotient group of a subgroup of the group. In this paper, we explain some of the properties of transfers by using noncommutative determinants. These properties enable us…