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

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

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

Social Capital, Institutions and Growth: Further Lessons from the Italian Regional Divide

Since Putnam's work on social capital, the Italian regional case has been a very rich source of both data and theories about the origins of large and persistent differences in local stocks of social capital, and about the impact of such differences on economic performances. The Italian case is widely interpreted as supporting the idea that persistent regional divides are largely explained by local differences in social capital. In this paper we maintain that this interpretation fails to recognize that the current large regional gap in Italy is significantly linked to two policy decisions taken by the central State at the beginning of the 1970s. In particular, we focus on the possibility that social capital became a binding constraint for the growth of southern Italy’s mainly as a consequence of the deep process of governmental decentralization that began in the1970s. We formalize this hypothesis by using an endogenous growth model with public capital. In this model, the accumulation of public capital is characterized by the presence of iceberg costs that depend on social capital. Decentralization affects these costs because the impact of the local stocks of social capital on public investment increases when the latter is managed locally. To assess the role of decentralization as a trigger of the influence of local social capital on growth, we control for the impact of labor market reforms, a second and almost simultaneous institutional shock that took place in Italy and that made regional labor markets far more rigid than in the previous decades. In the second part of our paper, we use the large empirical literature on the Italian regions to restrict the values of the parameters of our model in order to perform a simple simulation exercise. In this exercise, the model turns out to be able to account for the major swings in the convergence of southern regions towards the center-northern regions since 1861. The general lessons we can draw from this further analysis of the Italian regional case are as follows. First, we show that the strength of social capital as a determinant of long-run growth may depend on some well-defined characteristic of the institutional context. Second, our model suggests that the economic success of decentralization policies -- even when the budget constraint is not 'soft' -- depends on the local endowment of social capital.

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