Gravitational Structure Formation, the Cosmological Problem and Statistical Physics

Models of structure formation in the universe postulate that matter distributions observed today in galaxy catalogs arise, through a complex non-linear dynamics, by gravitational evolution from a very uniform initial state. Dark matter plays the central role of providing the primordial density seeds which will govern the dynamics of structure formation. We critically examine the role of cosmological dark matter by considering three different and related issues: Basic statistical properties of theoretical initial density fields, several elements of the gravitational many-body dynamics and key correlation features of the observed galaxy distributions are discussed, stressing some useful analogies with known systems in modern statistical physics.Comment: 5 pages 1 postscript figure. Proceeding of the conference Proceedings of the 3rd International Conference NEXT-SigmaPh

Statistical physics for cosmic structures

The recent observations of galaxy and dark matter clumpy distributions have provided new elements to the understating of the problem of cosmological structure formation. The strong clumpiness characterizing galaxy structures seems to be present in the overall mass distribution and its relation to the highly isotropic Cosmic Microwave Background Radiation represents a fundamental problem. The extension of structures, the formation of power-law correlations characterizing the strongly clustered regime and the relation between dark and visible matter are the key problems both from an observational and a theoretical point of view. We discuss recent progresses in the studies of structure formation by using concepts and methods of statistical physics.Comment: 8 pages, 4 figures, European Physical Journal B - STATPHYS 23 topical issue in the press (2007

Fractal structures and the large scale distribution of galaxies

Galaxy structures are certainly fractal up to a certain crossover scale \lambda_0. A clear determination of such a scale is still missing. Usually, the conceptual and practical implications of this property are neglected and the structures are only discussed in terms of their global amplitude. Here we present a compact summary of these implications. First, we discuss the problem of the identification of the crossover scale \lambda_0 and the proper characterization of the scaling. We then consider the implications of these properties with respect to various physical phenomena and to the corresponding characteristic values, i.e. r_0, \sigma_8, \Omega, etc. These implications crucially depend on the value of \lambda_0, but they are still important for a relatively small value, say \lambda_0 \approx 50 \hmp. Finally we consider the main theoretical consequences of these results.Comment: 27 pages, 3 figures. To appear in the proceedings of the 7th Course in astrofundamental physics, Nato Advanced Study Institute, International Euroconference Erice, 5-16 December 199

On the convergence of the Fitness-Complexity Algorithm

We investigate the convergence properties of an algorithm which has been recently proposed to measure the competitiveness of countries and the quality of their exported products. These quantities are called respectively Fitness F and Complexity Q. The algorithm was originally based on the adjacency matrix M of the bipartite network connecting countries with the products they export, but can be applied to any bipartite network. The structure of the adjacency matrix turns to be essential to determine which countries and products converge to non zero values of F and Q. Also the speed of convergence to zero depends on the matrix structure. A major role is played by the shape of the ordered matrix and, in particular, only those matrices whose diagonal does not cross the empty part are guaranteed to have non zero values as outputs when the algorithm reaches the fixed point. We prove this result analytically for simplified structures of the matrix, and numerically for real cases. Finally, we propose some practical indications to take into account our results when the algorithm is applied.Comment: 13 pages, 8 figure

Liquidity crises on different time scales

We present an empirical analysis of the microstructure of financial markets and, in particular, of the static and dynamic properties of liquidity. We find that on relatively large time scales (15 min) large price fluctuations are connected to the failure of the subtle mechanism of compensation between the flows of market and limit orders: in other words, the missed revelation of the latent order book breaks the dynamical equilibrium between the flows, triggering the large price jumps. On smaller time scales (30 s), instead, the static depletion of the limit order book is an indicator of an intrinsic fragility of the system, which is related to a strongly nonlinear enhancement of the response. In order to quantify this phenomenon we introduce a measure of the liquidity imbalance present in the book and we show that it is correlated to both the sign and the magnitude of the next price movement. These findings provide a quantitative definition of the effective liquidity, which proves to be strongly dependent on the considered time scales

Economic Development and Inequality: a complex system analysis

By borrowing methods from complex system analysis, in this paper we analyze the features of the complex relationship that links the development and the industrialization of a country to economic inequality. In order to do this, we identify industrialization as a combination of a monetary index, the GDP per capita, and a recently introduced measure of the complexity of an economy, the Fitness. At first we explore these relations on a global scale over the time period 1990--2008 focusing on two different dimensions of inequality: the capital share of income and a Theil measure of wage inequality. In both cases, the movement of inequality follows a pattern similar to the one theorized by Kuznets in the fifties. We then narrow down the object of study ad we concentrate on wage inequality within the United States. By employing data on wages and employment on the approximately 3100 US counties for the time interval 1990--2014, we generalize the Fitness-Complexity algorithm for counties and NAICS sectors, and we investigate wage inequality between industrial sectors within counties. At this scale, in the early nineties we recover a behavior similar to the global one. While, in more recent years, we uncover a trend reversal: wage inequality monotonically increases as industrialization levels grow. Hence at a county level, at net of the social and institutional factors that differ among countries, we not only observe an upturn in inequality but also a change in the structure of the relation between wage inequality and development