Stochastic model of Zipf's law and the universality of the power-law exponent.
We propose a stochastic model of Zipf's law, namely a power-law relation between rank and size, and clarify as to why a specific value of its power-law exponent is quite universal. We focus on the successive total of a multiplicative stochastic process. By employing properties of a well-known stochastic process, we concisely show that the successive total follows a stationary power-law distribution, which is directly related to Zipf's law. The formula of the power-law exponent is also derived. Finally, we conclude that the universality of the rank-size exponent is brought about by symmetry between an increase and a decrease in the random growth rate.
Department of Physics, Faculty of Science and Engineering, Chuo University, Kasuga 1-chome, Bunkyo, Tokyo, Japan.
Ken
K
Yamamoto