When the probability of measuring a particular value of some quantity varies
inversely as a power of that value, the quantity is said to follow a power law,
also known variously as Zipf's law or the Pareto distribution. Power laws
appear widely in physics, biology, earth and planetary sciences, economics and
finance, computer science, demography and the social sciences. For instance,
the distributions of the sizes of cities, earthquakes, solar flares, moon
craters, wars and people's personal fortunes all appear to follow power laws.
The origin of power-law behaviour has been a topic of debate in the scientific
community for more than a century. Here we review some of the empirical
evidence for the existence of power-law forms and the theories proposed to
explain them.
