Related papers: Isotropy, homogeneity and dipole saturation
The behaviour of elastic structures undergoing large deformations is the result of the competition between confining conditions, self-avoidance and elasticity. This combination of multiple phenomena creates a geometrical frustration that…
A map is given showing that convolutions of independent random variables over a finite group and matrix multiplications of doubly stochastic matrices are homomorphic. As an application, a short proof is given to the theorem that the…
This paper is concerned with sample path properties of isotropic Gaussian fields on compact two-point homogeneous spaces. In particular, we establish the property of strong local nondeterminism of an isotropic Gaussian field based on the…
We prove the existence and uniqueness of geometric models of local isometry classes of locally homogeneous spaces with sectional curvature $|\operatorname{sec}|\leq 1$. Moreover, we show that the set of geometric models is compact in the…
The question of the nature of galaxy clustering and the possible homogeneity of galaxy distribution is one of the fundamental problem of cosmology. It is well established that galaxy structures are characterized, up to a certain scale, by…
The situation of the decay of the metastable phase on the several types of heterogeneous centers is described analytically. The total number of heterogeneous centers is supposed to be equal for different types. This description decomposes…
It is shown that modular invariance provides a natural explanation for the absence of monopoles when assumed to be a discrete gauge symmetry. It follows that monopoles can not be seen because it is always possible to find a suitable…
If gamma-ray bursts are cosmological or in a halo distribution their properties are expected to be isotropic (at least to 1st order). However, our motion with respect to the burst parent population (whose proper frame is expected to be that…
In this note we study some properties of topological entropy for non-compact non-metrizable spaces. We prove that if a uniformly continuous self-map $f$ of a uniform space has topological shadowing property then the map $f$ has positive…
The large scale distribution of galaxies in the universe displays a complex pattern of clusters, super-clusters, filaments and voids with sizes limited only by the boundaries of the available samples. A quantitative statistical…
A topological space is iso-dense if it has a dense set of isolated points. A topological space is scattered if each of its non-empty subspaces has an isolated point. In $\mathbf{ZF}$, in the absence of the axiom of choice, basic properties…
We consider locally symmetric manifolds with a fixed universal covering, and construct for each such manifold M a simplicial complex R whose size is proportional to the volume of M. When M is non-compact, R is homotopically equivalent to M,…
Radiation traversing the observable universe provides powerful ways to probe anisotropy of electromagnetic propagation. A controversial recent study claimed a signal of dipole character. Here we test a new and independent data set of 361…
Scaling relations of galaxy clusters are a powerful probe of cosmic isotropy in the late Universe. Owing to their strong cosmological dependence, galaxy cluster scaling relations can obtain tight constraints on the spatial variation of…
Einstein's theory of gravitation that governs the geometry of space-time, coupled with spectacular advance in cosmological observations, promises to deliver a `standard model' of cosmology in the near future. However, local geometry of…
We decide the Borel complexity of the conjugacy problem for automorphism groups of countable homogeneous digraphs. Many of the homogeneous digraphs, as well as several other homogeneous structures, have already been addressed in previous…
In order to investigate whether galaxy structures are compatible with the predictions of the standard LCDM cosmology, we focus here on the analysis of several simple and basic statistical properties of the galaxy density field. Namely, we…
Modern cosmology rests on the cosmological principle, that on large enough scales the Universe is both homogeneous and isotropic. A corollary is that galaxies' spin vectors should be isotropically distributed on the sky. This has been…
There is an ongoing debate in cosmology about the value of the length scale at which ``homogeneity'' in the matter distribution is reached or even if such a scale exists. In the wake of this debate, we intend in this letter to clarify the…
How does the clustering of galaxies depend on their inner properties like morphological type and luminosity? We address this question in the mathematical framework of marked point processes and clarify the notion of luminosity and…