The privilege as the cause of power distributions in geophysics

Power laws are known to be associated with dynamic systems residing near the critical point in the state space of the system. However, both models, that of phase transitions reached by the tuning parameter (for example, the percolation models) and SOC (self-organised critical) models, although leading to power-law relations, still do not explaining causes of their appearance. In this contribution it is assumed that nature is random in its deep structure. The concept of the privilege, meaning the susceptibility of the state on to a change, is introduced. The model describing the privilege is analysed and applied to some known models: the Cantor set, the percolation theory and simple cellular automata. An adequate form of the privilege explains the appearance of the inverse-power distributions in many phenomena in geophysics. There is a relevance between the privilege concept and the results of a previous paper, in which the influence of the non-linearity of a model on the output behaviour was investigated.