Zipf's Law for Cities: An Explanation

Abstract

Zipf's law is a very tight constraint on the class of admissible models of local growth. It says that for most countries the size distribution of cities strikingly fits a power law: the number of cities with populations greater than <it>S</it> is proportional to 1/<it>S</it>. Suppose that, at least in the upper tail, all cities follow some proportional growth process (this appears to be verified emperically). This automatically leads their distribution to converge to Zipf's law.