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arXiv · 1602.08533

A Rank-Based Approach to Zipf's Law

Ricardo T. Fernholz·Robert Fernholz
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Abstract

An Atlas model is a rank-based system of continuous semimartingales for which the steady-state values of the processes follow a power law, or Pareto distribution. For a power law, the log-log plot of these steady-state values versus rank is a straight line. Zipf's law is a power law for which the slope of this line is -1. In this note, rank-based conditions are found under which an Atlas model will follow Zipf's law. An advantage of this rank-based approach is that it provides information about the dynamics of systems that result in Zipf's law.

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BibTeXRIS

Ricardo T. Fernholz, Robert Fernholz. 2016-02-27. A Rank-Based Approach to Zipf's Law. https://arxiv.org/abs/1602.08533

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