241 research outputs found
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
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