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

Frontiers in Physics

Kamihigashi, Takashi¹  Kumamoto, Shin-Ichiro¹ 

[1] Research Institute for Economics and Business Administration, Kobe University, Japan

关键词: power law;    Zipf';    s law;    Pareto';    s law;    Preferential attachment;    Geometric Brownian motion;    Multiplicative process;   

DOI  :  10.3389/fphy.2018.00020

学科分类：物理（综合）

来源: Frontiers

【 摘 要 】

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.

【 授权许可】

CC BY