Related papers: Persistent fluctuations and scaling properties in …
Fractal properties are usually characterized by means of various statistical tools which deal with spatial average quantities. Here we focus on the determination of fluctuations around the average counts and we develop a test for the study…
We present a brief introduction to the statistical properties of systems with large fluctuations. We point out that for such systems the relevant statistical quantities are scaling exponents and the nature of fluctuations is completely…
We introduce and study two new concepts which are essential for the quantitative analysis of the statistical quality of the available galaxy samples. These are the dilution effect and the small scale fluctuations. We show that the various…
We study statistical properties of galaxy structures in several samples extracted from the 2dF Galaxy Redshift Survey. In particular, we measured conditional fluctuations by means of the scale-length method and determined their probability…
Some years ago we proposed a new approach to the analysis of galaxy and cluster correlations based on the concepts and methods of modern statistical Physics. This led to the surprising result that galaxy correlations are fractal and not…
The properties of the galaxy distribution at large scales are usually studied using statistics which are assumed to be self-averaging inside a given sample. We present a new analysis able to quantitatively map galaxy large scale structures…
This paper presents an analysis of the smoothness problem in cosmology by focussing on the ambiguities originated in the simplifying hypotheses aimed at observationally verifying if the large-scale distribution of galaxies is homogeneous,…
The debate on the correlation properties of galaxy structures has having an increasing interest during the last year. In this lecture we discuss the claims of different authors who have criticized our approach and results. In order to have…
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…
I critically discuss in a pedagogical and phenomenological way a few crucial tests challenging the claims by Pietronero and collaborators that there is no evidence from available galaxy catalogues that the Universe is actually homogeneous…
We apply the scale-length method to several three dimensional samples of the Two degree Field Galaxy Redshift Survey. This method allows us to map in a quantitative and powerful way large scale structures in the distribution of galaxies…
The aim of this review article is to give a comprehensive description of the scaling properties detected for the distribution of cosmic structures. Due to the great variety of statistical methods to describe the large-scale structure of the…
We introduce the basic techniques used for the analysis of three dimensional and two dimensional galaxy samples. We report the correlation analysis of various redshift surveys which shows that the available data are consistent with each…
We characterize galaxy correlations in the Sloan Digital Sky Survey by measuring several moments of galaxy counts in spheres. We firstly find that the average counts grows as a power-law function of the distance with an exponent D= 2.1+-…
This comment is in response to the paper by L. Guzzo recently appeared in ``New Astronomy'' related to our work. The subject of the discussion concerns the correlation properties of galaxy distribution in the available 3-d samples. There is…
In the last years there has been a growing interest in the understanding a vast variety of scale invariant and critical phenomena occurring in nature. Experiments and observations indeed suggest that many physical systems develop…
There is a general agreement that galaxy structures exhibit fractal properties, at least up to some small scale. However the presence of an eventual crossover towards homogenization, as well as the exact value of the fractal dimension, are…
We report the correlation analysis of various redshift surveys which shows that the available data are consistent with each other and manifest fractal correlations (with dimension $D \simeq 2$) up to the present observational limits…
The properties of spatial distribution of luminous matter are investigated analysing all the available three dimensional catalogues of galaxies. In standard view, galaxies are believed to have a fractal distribution at small scale with a…
Precise analyses of the statistical and scaling properties of galaxy distribution are essential to elucidate the large-scale structure of the universe. Given the ongoing debate on its statistical features, the development of statistical…