%0 Unpublished Work %D 2019 %T Evasión en IVA: Análisis de redes %A Carlos Gershenson %A Gerardo Iñiguez %A Carlos Pineda %A Rita Guerrero %A Eduardo Islas %A Omar Pineda %A Martín Zumaya %G eng %U http://omawww.sat.gob.mx/gobmxtransparencia/Paginas/documentos/estudio_opiniones/Evasion_en_IVA_Analisis_de_Redes.pdf %0 Journal Article %J Physica A: Statistical Mechanics and its Applications %D 2019 %T Rank-frequency distribution of natural languages: A difference of probabilities approach %A Germinal Cocho %A Rosalío F. Rodríguez %A Sergio Sánchez %A Jorge Flores %A Carlos Pineda %A Carlos Gershenson %K Fokker–Planck equation %K Languages %K Master equation %K Rank dynamics %X In this paper we investigate the time variation of the rank k of words for six Indo-European languages using the Google Books N-gram Dataset. Based on numerical evidence, we regard k as a random variable whose dynamics may be described by a Fokker–Planck equation which we solve analytically. For low ranks the distinct languages behave differently, maybe due to the syntax rules, whereas for k>50 the law of large numbers predominates. We analyze the frequency distribution of words using the data and their adjustment in terms of time-dependent probability density distributions. We find small differences between the data and the fits due to conflicting dynamic mechanisms, but the data show a consistent behavior with our general approach. For the lower ranks the behavior of the data changes among languages presumably, again, due to distinct dynamic mechanisms. We discuss a possible origin of these differences and assess the novel features and limitations of our work. %B Physica A: Statistical Mechanics and its Applications %V 532 %P 121795 %G eng %U https://doi.org/10.1016/j.physa.2019.121795 %R 10.1016/j.physa.2019.121795