In the past twenty years observations have provided several three dimensional maps of galaxy distribution, from which there is a growing evidence of large scale structures. This important discovery has been possible thanks to the advent of large redshift surveys: angular galaxy catalogs are in fact essentially smooth and structure-less. In the figure above we show a slice of the Center for Astrophysics galaxy catalog (CfA2), which was completed in the early nineties, and a slice constructed from the recent observations of the Sloan Digital Sky Survey (SDSS) project. In the CfA2 catalog, which was one of the first maps surveying the local universe, it has been discovered the giant ``Great Wall'' a filament linking several groups and clusters of galaxies of extension of about 200 Mpc/h and whose size is limited by the sample boundaries. Recently the SDSS project has reveled the existence of structures larger than the Great Wall, and in particular in the figure above one may notice the so-called ``Sloan Great Wall'' which is almost double longer than the Great Wall. Nowadays this is the most extended structure ever observed, covering about 400 Mpc/h, and whose size is again limited by the boundaries of the sample.

The search for the ``maximum'' size of galaxy structures and voids, beyond which the distribution becomes essentially smooth, is still an open problem. Instead the fact that galaxy structures are strongly irregular and form complex patterns has become a well-established fact. From the theoretical point of view the understating of the statistical characterization of these structures represents the key element to be considered by a physical theory dealing with their formation. The primary questions that such a situation rises are therefore: (i) which is the nature of galaxy structures and (ii) which is the maximum size of structures ? A number of statistical concepts can be used to answer to these questions: in general one wants to characterize n-point correlation properties which are able to capture the main elements of points distributions

This subject is matter of a wide debate in the field and it can raise strong feelings as it touches the foundations of the field of theoretical cosmology. Our work however only concerns the determination of statistical properties and more importantly it is focused on the methods which are usually used to determine these properties. Thanks to our expertise in complex systems we have developed new statistical quantities and very focused tests for the case of galaxy structures. Indeed our results show that the main assumptions used in all statistical analyses applied up to now, namely the homogeneity and statistical stationarity in space of the relevant statistical quantities inside a given sample, is not verified in the samples considered.