The meaning of the power law distributions in describing complex systems: implications for social sciences

Power laws are a special class of functions, which have been demonstrated to describe a lot of natural, economic and social phenomena. They assume often the form of a probability distribution, but they have been also used to explain other occurrences like the geometrical growing of biological or social entities (i.e. trees, cities, enterprises, etc.). Starting from the description of the physical and mathematical reasons for their emergence, we present some outstanding properties of the power laws (for example the scale invariance) and we review several studies carried out in many research areas. We focus particularly on social studies, in order to demonstrate that the understanding of the mechanism of action of the power laws has impact on the performances in multi-agents contexts and on the prevention of potentially disastrous events. First results on the extension to the Italian context of previous studies are also shown.