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Size-dependent word frequencies and translational invariance of books

Author

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  • Bernhardsson, Sebastian
  • da Rocha, Luis Enrique Correa
  • Minnhagen, Petter

Abstract

It is shown that a real novel shares many characteristic features with a null model in which the words are randomly distributed throughout the text. Such a common feature is a certain translational invariance of the text. Another is that the functional form of the word-frequency distribution of a novel depends on the length of the text in the same way as the null model. This means that an approximate power-law tail ascribed to the data will have an exponent which changes with the size of the text-section which is analyzed. A further consequence is that a novel cannot be described by text-evolution models such as the Simon model. The size-transformation of a novel is found to be well described by a specific Random Book Transformation. This size transformation in addition enables a more precise determination of the functional form of the word-frequency distribution. The implications of the results are discussed.

Suggested Citation

  • Bernhardsson, Sebastian & da Rocha, Luis Enrique Correa & Minnhagen, Petter, 2010. "Size-dependent word frequencies and translational invariance of books," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(2), pages 330-341.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:2:p:330-341
    DOI: 10.1016/j.physa.2009.09.022
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    References listed on IDEAS

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    1. Gonçalves, L.L. & Gonçalves, L.B., 2006. "Fractal power law in literary English," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(2), pages 557-575.
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    Cited by:

    1. Çavuşoğlu, Abdullah & Türker, İlker, 2014. "Patterns of collaboration in four scientific disciplines of the Turkish collaboration network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 220-229.
    2. Yan, Xiaoyong & Minnhagen, Petter, 2016. "Randomness versus specifics for word-frequency distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 828-837.
    3. Yan, Xiaoyong & Minnhagen, Petter, 2018. "The dependence of frequency distributions on multiple meanings of words, codes and signs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 554-564.

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