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arXiv · 1811.09451

Rank-frequency distribution of natural languages: a difference of probabilities approach

Germinal Cocho·R. F. Rodríguez·Sergio Sánchez·Jorge Flores·Carlos Pineda·Carlos Gershenson
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Abstract

The time variation of the rank $k$ of words for six Indo-European languages is obtained using data from Google Books. For low ranks the distinct languages behave differently, maybe due to syntaxis rules, whereas for $k>50$ the law of large numbers predominates. The dynamics of $k$ is described stochastically through a master equation governing the time evolution of its probability density, which is approximated by a Fokker-Planck equation that is solved analytically. The difference between the data and the asymptotic solution is identified with the transient solution, and good agreement is obtained.

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Germinal Cocho, R. F. Rodríguez, Sergio Sánchez, Jorge Flores, Carlos Pineda, Carlos Gershenson. 2018-11-23. Rank-frequency distribution of natural languages: a difference of probabilities approach. https://doi.org/10.1016/j.physa.2019.121795

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