Related papers: Persistent fluctuations and scaling properties in …
It is shown that the observed fractal distribution of galaxies is, in fact, consistent with homogeneity of the Universe and observational limits on $ \Delta T/T$, if the presence of dark matter and dark charge predicted by the Modified…
Evidence is presented that the galaxy distribution can be described as a fractal system in the redshift range of the FDF galaxy survey. The fractal dimension $D$ was derived using the FDF galaxy volume number densities in the spatially…
Cosmic structures at large scales represent the earliest and most extended form of matter condensation. In this lecture we review the application of the methods and concepts of modern statistical physics to these structures. This leads to a…
Large self-gravitating stellar systems share with correlated liquids in condensed matter physics a pattern of hierarchical density variations. While it takes the microscopic time resolution to discern the correlated dynamics of the critical…
We give the first determination of the observed peculiar velocity distribution function for a representative sample of galaxies (within 50 Mpc (H=100) of the Local Group), which includes a wide range of clustering properties. We explore in…
The fractal structure of star formation on large scales in disk galaxies is studied using the size distribution function of stellar aggregates in kpc-scale star fields. Achival HST images of 10 galaxies are Gaussian smoothed to define the…
The variability of temporal (or spatial) fluctuations of any variable is represented in conventional statistical theory by the relative dispersion equal to the standard deviation divided by the mean . The Relative Dispersion decreases with…
In this lecture we clarify the basic difference between the correlation properties for systems characterized by small or large fluctuations. The concepts of correlation length, homogeneity scale, scale invariance and criticality are…
The fluctuation scaling law has universally been observed in a wide variety of phenomena. For counting processes describing the number of events occurred during time intervals, it is expressed as a power function relationship between the…
We study the role of finiteness and fluctuations about average quantities for basic structural properties of growing networks. We first determine the exact degree distribution of finite networks by generating function approaches. The…
A large population of extended substructures generates a stochastic gravitational field that is fully specified by the function $p({\bf F})$, which defines the probability that a tracer particle experiences a force $\bf F$ within the…
The spatial distribution of galaxies we observed is subject to the given condition that we, human beings are sitting right in a galaxy -- the Milky Way. Thus the ergodicity assumption is questionable in interpretation of the observed galaxy…
The frequency of occurrence of prime numbers at unit number spacing intervals exhibits selfsimilar fractal fluctuations concomitant with inverse power law form for power spectrum generic to dynamical systems in nature such as fluid flows,…
This work discusses the possible empirical verification of the geometrical concept of homogeneity of the standard relativistic cosmology considering its various definitions of distance. We study the physical consequences of the distinction…
Next generation surveys will provide us with an unprecedented number of detections of supernovae Type Ia and gravitational wave merger events. Cross-correlations of such objects offer novel and powerful insights into the large-scale…
Estimates of the fractal dimension $D$ of the set of galaxies in the universe, based on ever improving data sets, tend to settle on $D\approx 2$. This result raised a raging debate due to its glaring contradiction with astrophysical models…
An approach is suggested for treating multiscale fluctuations in macromolecular systems. The emphasis is on the statistical properties of such fluctuations. The approach is illustrated by a macromolecular system with mesoscopic fluctuations…
Inhomogeneities in deposition may lead to formation of rough surfaces, whose height fluctuations can be probed directly by scanning microscopy, or indirectly by scattering. Analytical or numerical treatments of simple growth models suggest…
Several recent studies have shown how to properly calculate the observed clustering of galaxies in a relativistic context, and uncovered corrections to the Newtonian calculation that become significant on scales near the horizon. Here, we…
Source confusion has been a long-standing problem in the astronomical history. In the previous formulation, sources are assumed to be distributed homogeneously on the sky. This fundamental assumption is not realistic in many applications.…