Universality of Zipf's Law

TL;DR

This paper presents a simple, universal model that explains why Zipf's law appears across various systems by modeling its evolution as a random walk in logarithmic space.

Contribution

The paper introduces a generic model that reproduces Zipf's law and provides a theoretical explanation for its robustness and universality.

Findings

Model reproduces Zipf's law across different systems

Random walk in log scale explains Zipf's law emergence

Behavior is shown to be robust and universal

Abstract

We introduce a simple and generic model that reproduces Zipf's law. By regarding the time evolution of the model as a random walk in the logarithmic scale, we explain theoretically why this model reproduces Zipf's law. The explanation shows that the behavior of the model is very robust and universal.