The variation of Zipf's law in human language

@article{Cancho2005TheVO,
  title={The variation of Zipf's law in human language},
  author={Ramon Ferrer i Cancho},
  journal={European Physical Journal B},
  year={2005},
  volume={44},
  pages={249-257}
}
  • R. F. Cancho
  • Published 20 April 2005
  • Computer Science
  • European Physical Journal B
Words in humans follow the so-called Zipf’s law. More precisely, the word frequency spectrum follows a power function, whose typical exponent is β≈2, but significant variations are found. We hypothesize that the full range of variation reflects our ability to balance the goal of communication, i.e. maximizing the information transfer and the cost of communication, imposed by the limitations of the human brain. We show that the higher the importance of satisfying the goal of communication, the… 
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References

SHOWING 1-10 OF 70 REFERENCES
Least effort and the origins of scaling in human language
  • R. F. Cancho, R. Solé
  • Physics
    Proceedings of the National Academy of Sciences of the United States of America
  • 2003
TLDR
This article explains how language evolution can take advantage of a communicative phase transition and suggests that Zipf's law is a hallmark of symbolic reference and not a meaningless feature.
Two Regimes in the Frequency of Words and the Origins of Complex Lexicons: Zipf’s Law Revisited*
TLDR
It is made evident that word frequency as a function of the rank follows two different exponents, ˜(-)1 for the first regime and ™(-)2 for the second.
Quantitative Linguistics and Complex System Studies
TLDR
Linguistic discourses treated as maximum entropy systems of words according to prescriptions of algorithmic information theory are shown to give a natural explanation of Zipf's law with quantitative rigor and are likely to be valid for diverse complex systems of nature.
The evolution of syntactic communication
TLDR
A model for the population dynamics of language evolution is presented, the basic reproductive ratio of words and the maximum size of a lexicon are defined and the number of required signals exceeds a threshold value is calculated.
The basic reproductive ratio of a word, the maximum size of a lexicon.
  • M. Nowak
  • Linguistics
    Journal of theoretical biology
  • 2000
TLDR
A mathematical framework is constructed for the population dynamics of language evolution with particular emphasis on how words are propagated over generations, and an upper limit is obtained for the number of words in a language that relies exclusively on oral transmission.
Major Transitions in Language Evolution
TLDR
This paper uses mathematical models to analyzethe major transitions in language evolution and discusses the evolution ofcoordinated associations between signals and objects in a population, and analyzes the population dynamics of words and the adaptive emergence of syntax.
...
...