基于秩的Zipf定律方法
A Rank-Based Approach to Zipf's Law
AI总结：
本文提出基于秩的条件，使Atlas模型遵循Zipf定律，通过分析秩与稳态值的关系，揭示系统动态机制。
摘要：
Atlas模型是一种连续半鞅的秩为基础的系统，其稳态值遵循幂律或帕累托分布。对于幂律，稳态值与秩的对数对数图是一条直线。Zipf定律是其中斜率为-1的幂律。本文发现使Atlas模型遵循Zipf定律的秩条件。这种方法的优势在于提供了导致Zipf定律的系统动态信息。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
