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700396.pdf (1.15 MB)

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2020-02-05

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cc-by (c) Corral, Álvaro et al., 2020
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/173736

From Boltzmann to Zipf through Shannon and Jaynes

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Recurs relacionat

https://doi.org/10.3390/e22020179

Resum

The word-frequency distribution provides the fundamental building blocks that generate discourse in natural language. It is well known, from empirical evidence, that the word-frequency distribution of almost any text is described by Zipf's law, at least approximately. Following Stephens and Bialek (2010), we interpret the frequency of any word as arising from the interaction potentials between its constituent letters. Indeed, Jaynes' maximum-entropy principle, with the constrains given by every empirical two-letter marginal distribution, leads to a Boltzmann distribution for word probabilities, with an energy-like function given by the sum of the all-to-all pairwise (two-letter) potentials. The so-called improved iterative-scaling algorithm allows us finding the potentials from the empirical two-letter marginals. We considerably extend Stephens and Bialek's results, applying this formalism to words with length of up to six letters from the English subset of the recently created Standardized Project Gutenberg Corpus. We find that the model is able to reproduce Zipf's law, but with some limitations: the general Zipf's power-law regime is obtained, but the probability of individual words shows considerable scattering. In this way, a pure statistical-physics framework is used to describe the probabilities of words. As a by-product, we find that both the empirical two-letter marginal distributions and the interaction-potential distributions follow well-defined statistical laws.

Matèries

Entropia, Lingüística matemàtica, Distribució (Teoria de la probabilitat), Probabilitats

Matèries (anglès)

Entropy, Mathematical linguistics, Distribution (Probability theory), Probabilities

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Col·leccions

Articles publicats en revistes (Física de la Matèria Condensada)

Citació

CORRAL, Álvaro and GARCÍA DEL MURO Y SOLANS, Montserrat. From Boltzmann to Zipf through Shannon and Jaynes. Entropy. 2020. Vol. 22(2), num. 179. ISSN 1099-4300. [consulted: 11 of August of 2026]. Available at: https://hdl.handle.net/2445/173736

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