TY - JOUR T1 - Rank-frequency distribution of natural languages: A difference of probabilities approach JF - Physica A: Statistical Mechanics and its Applications Y1 - 2019 A1 - Germinal Cocho A1 - Rosalío F. Rodríguez A1 - Sergio Sánchez A1 - Jorge Flores A1 - Carlos Pineda A1 - Carlos Gershenson KW - Fokker–Planck equation KW - Languages KW - Master equation KW - Rank dynamics AB - 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. VL - 532 UR - https://doi.org/10.1016/j.physa.2019.121795 ER -