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Front. Phys. | doi: 10.3389/fphy.2018.00020

Power Laws in Stochastic Processes for Social Phenomena: An Introductory Review

 Shin-Ichiro Kumamoto1* and Takashi Kamihigashi1
  • 1Kobe University, Japan

Many phenomena with power laws have been observed in various fields of the natural and social sciences, and these power laws are often interpreted as the macro behaviors of systems that consist of micro units. In this paper, we review some basic mathematical mechanisms that are known to generate power laws.
In particular, we focus on stochastic processes including the Yule process and the Simon process as well as some recent models.
The main purpose of this paper is to explain the mathematical details of their mechanisms in a self-contained manner.

Keywords: power law, Zipf's law, Pareto's law, Preferential attachment, Geometric Brownian motion, Multiplicative process

Received: 13 Oct 2017; Accepted: 14 Feb 2018.

Edited by:

Isamu Okada, Sōka University, Japan

Reviewed by:

Renaud Lambiotte, University of Oxford, United Kingdom
Francisco W. Lima, Federal University of Piauí, Brazil  

Copyright: © 2018 Kumamoto and Kamihigashi. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: PhD. Shin-Ichiro Kumamoto, Kobe University, Kobe, Japan,