Power-law distributions resulting from finite resources

An elementary stochastic model, termed the normalization model, is put forward which does demonstrate that power-laws generically occur in systems with finite resources. The model is capable to exhibit power-law distributions with arbitrary power law exponents; nevertheless, for a large fraction of the parameter space power law exponents near unity are obtained. As an application of the normalization mechanism we consider a network growth-saturation model. This model extends the scale-free network model (SF) to include the fact of finite resources. In the network growth-saturation model the scale-free property holds only for the growth period, within the stationary regime we obtain power-law distributions of the weight of the edges among the vertices. We conjecture that this pattern will be found in the Internet if it reaches the steady state.