Related papers: Hyperuniform point sets on flat tori: deterministi…
We study a generalisation of the concept of hyperuniformity to spheres of arbitrary dimension. It is shown that QMC-designs (and especially spherical designs) are hyperuniform in our sense.
The concept of hyperuniformity has been introduced by Torquato and Stillinger in 2003 as a notion to detect structural behaviour intermediate between amorphous disorder and crystalline order. The present paper studies a generalisation of…
We extend the notion of hyperuniformity to the projective spaces $\mathbb{RP}^{d-1}$, $\mathbb{CP}^{d-1}$, $\mathbb{HP}^{d-1}$, and $\mathbb{OP}^2$. We show that hyperuniformity implies uniform distribution and present examples of…
When modeling directional data, that is, unit-norm multivariate vectors, a first natural question is to ask whether the directions are uniformly distributed or, on the contrary, whether there exist modes of variation significantly different…
In this work we present a study on the characterization of ordered and disordered hyperuniform point distributions on spherical surfaces. In spite of the extensive literature on disordered hyperuniform systems in Euclidean geometries, to…
We study hyperuniform properties in various two-dimensional periodic and quasiperiodic point patterns. Using the histogram of the two-point distances, we develop an efficient method to calculate the hyperuniformity order metric, which…
We propose a projection-based class of uniformity tests on the hypersphere using statistics that integrate, along all possible directions, the weighted quadratic discrepancy between the empirical cumulative distribution function of the…
Let X be an irreducible, reduced complex projective hypersurface of degree d. A uniform point for X is a point P such that the projection of X from P has maximal monodromy. We extend and improve some results concerning the finiteness of the…
A spatial distribution is hyperuniform if it has local density fluctuations that vanish in the limit of long length scales. Hyperuniformity is a well known property of both crystals and quasicrystals. Of recent interest, however, is…
We construct flat metrics in a given conformal class with prescribed singularities of real orders at marked points of a closed real surface. The singularities can be small conical, cylindrical, and large conical with possible translation…
Hyperuniform particle arrangements are characterized by a local number variance that grows more slowly than the volume of the observation window. We generalize this concept to describe particle systems in which particles carry weights:…
The discrepancy of a point set quantifies how well the points are distributed, with low-discrepancy point sets demonstrating exceptional uniform distribution properties. Such sets are integral to quasi-Monte Carlo methods, which approximate…
Uniform probability distributions on $\ell_p$ balls and spheres have been studied extensively and are known to behave like product measures in high dimensions. In this note we consider the uniform distribution on the intersection of a…
Hyperuniformity, the suppression of density fluctuations at large length scales, is observed across a wide variety of domains, from cosmology to condensed matter and biological systems. Although the standard definition of hyperuniformity…
In this note we will consider the question when from the appropriate behavior of a sequence of points on caps we can conclude that the sequence is uniformly distributed on the sphere.
We introduce a rigorous and sensitive significance test for hyperuniformity that yields reliable results even from a single sample. Our approach is based on a detailed analysis of the empirical Fourier transform of a stationary point…
Hyperuniformity is the study of stationary point processes with a sub-Poisson variance in a large window. In other words, counting the points of a hyperuniform point process that fall in a given large region yields a small-variance Monte…
We study the variance in the number of points contained within a window $\Omega$ of arbitrary size, and to further illuminate our understanding of {\it hyperuniform} systems, i.e., point patterns that do not possess long-wavelength…
Hyperuniformity refers to the suppression of density fluctuations at large scales. Typical for ordered systems, this property also emerges in several disordered physical and biological systems, where it is particularly relevant to…
Hyperuniform structures are disordered, correlated systems in which density fluctuations are suppressed at large scales. Such a property generalizes the concept of order in patterns and is relevant across diverse physical systems. We…