Zipf’s law for atlas models

  title={Zipf’s law for atlas models},
  author={Ricardo T. Fernholz and Robert Fernholz},
  journal={Journal of Applied Probability},
  pages={1276 - 1297}
Abstract A set of data with positive values follows a Pareto distribution if the log–log plot of value versus rank is approximately a straight line. A Pareto distribution satisfies Zipf’s law if the log–log plot has a slope of $-1$. Since many types of ranked data follow Zipf’s law, it is considered a form of universality. We propose a mathematical explanation for this phenomenon based on Atlas models and first-order models, systems of strictly positive continuous semimartingales with… 
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