Zipf's Law Arises Naturally When There Are Underlying, Unobserved Variables

Area of Science:

• Statistical physics
• Data science
• Computational neuroscience

Background:

• Zipf's law describes an inverse relationship between an observation's probability and its rank.
• Existing explanations for Zipf's law are often domain-specific.
• Statistical physics methods have recently offered a general explanation for Zipf's law.

Purpose of the Study:

• To provide a simpler, more intuitive, and broadly applicable explanation of Zipf's law.
• To develop methods for verifying the applicability of this explanation to specific datasets.
• To empirically extend the explanation to diverse data types.

Main Methods:

• Theoretical extension of statistical physics models for Zipf's law.
• Development of verification methods for model applicability.
• Empirical analysis of word frequencies, variable sequence length data, and multi-neuron spiking activity.

Main Results:

• A simplified and generalized theoretical explanation for Zipf's law was developed.
• Methods for verifying the applicability of the explanation were established.
• The explanation was successfully extended to word frequencies, variable sequence length data, and multi-neuron spiking activity.

Conclusions:

• Latent variable mixing provides a generalizable framework for understanding Zipf's law across domains.
• The simplified model enhances the understanding and applicability of Zipf's law.
• This work bridges theoretical insights from statistical physics with empirical validation in key data domains.