2003/03/18 by Kenji Kawamura, Naomichi Hatano, Kawamura, Kenji +1
Physics and Astronomy · #Complex Network Analysis Techniques #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Opinion Dynamics and Social Influence #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0303331
25 pages, figures included
arxiv created 2003/03/18 · openalex publication_date 2003/03/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Power-law distributions with various exponents are studied. We first introduce a simple and generic model that reproduces Zipf's law. We can regard this model both as the time evolution of the population of cities and that of the asset distribution. We show that our model is very robust against various variations. Next, we explain theoretically why our model reproduces Zipf's law. By considering the time-evolution equation of our model, we see that the essence of Zipf's law is an asymmetric random walk in a logarithmic scale. Finally, we extend our model by introducing an additional asymmetry. We show that the extended model reproduces various power-law exponents. By extending the theoretical argument for Zipf's law, we find a simple equation of the power-law exponent.