title: Rank diversity of languages: generic behavior in computational linguistics.
abstract: Statistical studies of languages have focused on the rank-frequency distribution of words. Instead, we introduce here a measure of how word ranks change in time and call this distribution rank diversity. We calculate this diversity for books published in six European languages since 1800, and find that it follows a universal lognormal distribution. Based on the mean and standard deviation associated with the lognormal distribution, we define three different word regimes of languages: "heads" consist of words which almost do not change their rank in time, "bodies" are words of general use, while "tails" are comprised by context-specific words and vary their rank considerably in time. The heads and bodies reflect the size of language cores identified by linguists for basic communication. We propose a Gaussian random walk model which reproduces the rank variation of words in time and thus the diversity. Rank diversity of words can be understood as the result of random variations in rank, where the size of the variation depends on the rank itself. We find that the core size is similar for all languages studied.
authors: Instituto de Física, Universidad Nacional Autónoma de México, Mexico City, Mexico; Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, Mexico City, Mexico.
authors: Germinal
authors: G
authors: Cocho
authors: Instituto de Física, Universidad Nacional Autónoma de México, Mexico City, Mexico.
authors: Jorge
authors: J
authors: Flores
authors: Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Mexico City, Mexico; Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, Mexico City, Mexico.
authors: Carlos
authors: C
authors: Gershenson
authors: Instituto de Física, Universidad Nacional Autónoma de México, Mexico City, Mexico.
authors: Carlos
authors: C
authors: Pineda
authors: Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico City, Mexico.
authors: Sergio
authors: S
authors: Sánchez
mesh_terms: D005060:Europe; D006801:Humans; D008037:Linguistics; D008962:Models, Theoretical