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Funktsional'nyi Analiz i ego Prilozheniya, 2014, Volume 48, Issue 2, Pages 51–66
DOI: https://doi.org/10.4213/faa3141 (Mi faa3141) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Zipf's Law and L. Levin Probability Distributions

Yu. I. Manin

Max Planck Institute for Mathematics
Full-text PDF (230 kB) Citations (10)
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DOI: https://doi.org/10.4213/faa3141
Abstract: Zipf's law in its basic incarnation is an empirical probability distribution governing the frequency of usage of words in a language. As Terence Tao recently remarked, it still lacks a convincing and satisfactory mathematical explanation.
In this paper I suggest that, at least in certain situations, Zipf's law can be explained as a special case of the a priori distribution introduced and studied by L. Levin. The Zipf ranking corresponding to diminishing probability appears then as the ordering by growing Kolmogorov complexity.
One argument justifying this assertion is the appeal to a recent interpretation by Yu. Manin and M. Marcolli of asymptotic bounds for error-correcting codes in terms of phase transition. In the respective partition function, the Kolmogorov complexity of a code plays the role of its energy.
Keywords: Zipf's law, Kolmogorov complexity.
Received: 13.08.2013
English version:
Functional Analysis and Its Applications, 2014, Volume 48, Issue 2, Pages 116–127
DOI: https://doi.org/10.1007/s10688-014-0052-1
Bibliographic databases:
Document Type: Article
UDC: 519.1+519.2
Language: Russian
Citation: Yu. I. Manin, “Zipf's Law and L. Levin Probability Distributions”, Funktsional. Anal. i Prilozhen., 48:2 (2014), 51–66; Funct. Anal. Appl., 48:2 (2014), 116–127
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/faa/v48/i2/p51
    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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