Related papers: Scaling and fluctuations in galaxy distribution: t…
Many fluctuating systems consist of macroscopic structures in addition to noisy signals. Thus, for this class of fluctuating systems, the scaling behaviors are very complicated. Such phenomena are quite commonly observed in Nature, ranging…
We aim to quantify the capability of the inhomogeneous distribution of galaxy clusters, represented by the two-point statistics in Fourier space, to retrieve information on the underlying scaling relations. We make a case study using the…
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…
A geometric approach to critical fluctuations of a nonequilibrium model is reported. The two-dimensional majority vote model was investigated by Monte Carlo simulations on square lattices of various sizes and a detailed scaling analysis of…
Universal scaling laws of fluctuations (the $\Delta$-scaling laws) can be derived for equilibrium and off-equilibrium systems when combined with the finite-size scaling analysis. In any system in which the second-order critical behavior can…
Fluctuation scaling is observed phenomenon from complex networks through finance to ecology. It means that the variance and the mean of a specific quantity are related as $\ev{\sigma^2|n}\propto \ev{n|A}^{2\alpha}$ with $1/2\geq \alpha \geq…
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…
This thesis focuses on characterizing the distribution of points and galaxies using multifractal analysis. In this attempt the main emphasis is on calculating the Minkowski-Bouligand fractal dimension (Dq) of the distribution of points over…
Observations of the clustering of galaxies can provide useful information about the distribution of dark matter in the Universe. In order to extract accurate cosmological parameters from galaxy surveys, it is important to understand how the…
In this introductory talk we will establish connections between the statistical analysis of galaxy clustering in cosmology and recent work in mainstream spatial statistics. The lecture will review the methods of spatial statistics used by…
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…
Catalogues of galaxies, clusters of galaxies and superclusters - sources of information to study the large-scale structure of the Universe are reviewed. The power spectrum of density perturbations, and the correlation function are discussed…
A detailed analysis of the galaxy distribution in the Southern Sky Redshift Survey (SSRS) by means of the multifractal or scaling formalism is presented. It is shown that galaxies cluster in different ways according to their morphological…
Well-calibrated scaling relations between the observable properties and the total masses of clusters of galaxies are important for understanding the physical processes that give rise to these relations. They are also a critical ingredient…
One of the main problems of observational cosmology is to determine the range in which a reliable measurement of galaxy correlations is possible. This corresponds to determine the shape of the correlation function, its possible evolution…
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…
Statistical analyses of finite sample distributions usually assume that fluctuations are self-averaging, i.e. that they are statistically similar in different regions of the given sample volume. By using the scale-length method, we test…
A new approach to the study of the large-scale stellar cluster distribution in the Galaxy based on two-point correlation techniques is presented. The basic formalism for this method is outlined and its applications are then investigated by…
In hierarchical models, density fluctuations on different scales are correlated. This induces correlations between dark halo masses, their formation histories, and their larger-scale environments. In turn, this produces a correlation…
Galaxy clustering provides a powerful way to probe cosmology. This requires understanding of the background mean density of galaxy samples, which is estimated from the survey itself by averaging the observed galaxy number density over the…