Geodesic
Zipf's Law and L.~Levin Probability Distributions
Funkcionalʹnyj analiz i ego priloženiâ, Tome 48 (2014) no. 2, pp. 51-66

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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. 
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     author = {Yu. I. Manin},
     title = {Zipf's {Law} and {L.~Levin} {Probability} {Distributions}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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Yu. I. Manin. Zipf's Law and L.~Levin Probability Distributions. Funkcionalʹnyj analiz i ego priloženiâ, Tome 48 (2014) no. 2, pp. 51-66. http://geodesic.mathdoc.fr/item/FAA_2014_48_2_a2/