Stochastic aggregation model for the multifractal distribution of matter

Two main features of the observable distribution of visible matter are the space correlations of galaxy positions and the mass function of galaxies. As discussed in Pietronero and Sylos Labini on this issue ([1], see also [2],[3]), the concept of multifractal (MF) distribution (including the masses) naturally unifies these two properties. Hence with the knowledge of the whole MF spectrum one obtains information on the correlations in space as well as on the mass function. From a theoretical point of view one would like to identify the dynamical process that leads to such a MF distribution. In order to gain some insight into this complex problem we have developed a simple stochastic model that includes some of the basic properties of aggregation process and allows us to pose a variety of interesting question concerning the possible dynamical origin of the MF distribution. The dynamics is characterised by some parameters, that have a direct physical meaning in term of cosmological processes. In this way we can relate the input parameters of the dynamics to the properties of the final configuration and produce a sort of phase diagram.