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Explaining Zipf's law via a mental lexicon.

Armen E Allahverdyan1, Weibing Deng2, Q A Wang3

  • 1Laboratoire de Physique Statistique et Systèmes Complexes, ISMANS, 44 ave. Bartholdi, 72000 Le Mans, France and Yerevan Physics Institute, Alikhanian Brothers Street 2, Yerevan 375036, Armenia.

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Summary

Zipf's law, a key linguistic regularity, can be explained by random word selection probabilities. This approach also accounts for word frequency distributions and relates to the author's mental lexicon via Bayesian statistics.

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Area of Science:

  • Statistical linguistics
  • Natural language processing
  • Computational linguistics

Background:

  • Zipf's law is a fundamental principle in statistical linguistics, describing rank-frequency distributions.
  • It serves as a model for scaling laws across various natural sciences.
  • Understanding the origins of Zipf's law is crucial for linguistic analysis.

Purpose of the Study:

  • To derive Zipf's law from basic probabilistic assumptions.
  • To explain the applicability of Zipf's law to single texts and its generalizations.
  • To connect the statistical properties of text to the author's cognitive processes.

Main Methods:

  • Modeling word occurrences as random draws with specific probabilities.
  • Applying Bayesian statistics to link a priori word densities to the mental lexicon.
  • Analyzing rank-frequency distributions, including high and low frequencies and hapax legomena.

Main Results:

  • Zipf's law can be mathematically derived from the assumption of random word probabilities.
  • The model successfully explains the applicability and generalizations of Zipf's law.
  • A direct relationship is established between word a priori density and the author's mental lexicon.

Conclusions:

  • The statistical regularities of language, like Zipf's law, can emerge from simple probabilistic mechanisms.
  • This provides a novel theoretical framework for understanding word frequency distributions.
  • The findings offer insights into the cognitive underpinnings of language production.