Related papers: A note on correlation and local dimensions
We compute the Hausdorff, upper box and packing dimensions for certain inhomogeneous Moran set constructions. These constructions are beyond the classical theory of iterated function systems, as different nonlinear contraction…
We consider Lorentzian manifolds as examples of partially ordered measure spaces, sets endowed with compatible partial order relations and measures, in this case given by the causal structure and the volume element defined by each…
We present a construction of a compact connected space which supports a normal probability measure.
Recent advances are being discussed on the calculation, within the conformal field theory approach, of the correlation functions for local operators in the theory of 2D gravity coupled to the minimal models of matter.
The local dimension spectrum provides a framework for quantifying the fractal properties of a measure, and it is well understood for non-overlapping self-similar measures. In this article, we study the local dimension spectrum for dominated…
We report on a few interrelations between bi-Hermitian metrics and locally conformally K\"ahler metrics on complex surfaces.
Quantitatively accurate electronic structure calculations rely on the proper description of electron correlation. A judicious choice of the approximate quantum chemistry method depends upon the importance of dynamic and nondynamic…
We study the local dimensions and local multifractal properties of measures on doubling metric spaces. Our aim is twofold. On one hand, we show that there are plenty of multifractal type measures in all metric spaces which satisfy only mild…
Local porosity distributions for a three-dimensional porous medium and local porosity distributions for a two-dimensional plane-section through the medium are generally different. However, for homogeneous and isotropic media having finite…
In quantum mechanics, spatial correlations arising from measurements at separated particles are well studied. This is not the case, however, for the temporal correlations arising from a single quantum system subjected to a sequence of…
We evaluate the localization length of the wave solution of a random potential characterized by an arbitrary autocorrelation function. We go beyond the Born approximation to evaluate the localization length using a non-linear approximation…
It is found that the measurement disturbance relation (MDR) determines the strength of quantum correlation and hence is one of the essential facets of the nature of quantum nonlocality. In reverse, the exact form of MDR may be ascertained…
A statistical measure is given expressing relative occurrences of quantities within a given data set. Application of this measure on several real life physical data sets and some abstract distributions are shown to yield consistent results.…
The verification and quantification of experimentally created entanglement by simple measurements, especially between distant particles, is an important basic task in quantum processing. When composite systems are subjected to local…
In this note, we introduce a new poset parameter called local $t$-dimension. We also discuss the fractional variants of this and other dimension-like parameters.
Everett's concept of relative state can be viewed as a map that contains information about correlations between measurement outcomes on two quantum systems. We demonstrate how geometric properties of the relative state map can be used to…
We show from a categorical point of view that probability measures on certain measurable or topological spaces arise canonically as the extension of probability distributions on countable sets. We do this by constructing probability monads…
We study some new invariant measures arising from local inverse iterates. Examples are also given.
The partial correlation coefficient is a commonly used measure to assess the conditional dependence between two random variables. We provide a thorough explanation of the partial copula, which is a natural generalization of the partial…
Open discrete mappings with a modulus condition in metric spaces are considered. Some results related to local behavior of mappings as well as theorems about continuous extension to a boundary are proved.