Mechanisms for Power Laws

Abstract

Power law distributions are ubiquitous statistical features of natural systems and are found in many different scientific disciplines. Indeed, many natural phenomena have power law size distributions reading, in the notation of Chap. 4, 14.1{\$}{\$}P(x) {\backslash}propto {\backslash}frac{\{}1{\}}{\{}{\{}{\{}x^1{\}} + {\backslash}mu {\}}{\}}{\$}{\$}up to some large limiting cut-off [463, 7, 607]. In expression (14.1), P(x)dx is the probability to observe the variable in the range between x and x + dx. Power laws seem to also describe a large ensemble of social and economic statistics [553, 828, 461, 233, 792, 469, 470, 29].