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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
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
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
Linking options:
https://www.mathnet.ru/eng/faa3141https://doi.org/10.4213/faa3141 https://www.mathnet.ru/eng/faa/v48/i2/p51
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