@article {Cocho2019,
	title = {Rank-frequency distribution of natural languages: A difference of probabilities approach},
	journal = {Physica A: Statistical Mechanics and its Applications},
	volume = {532},
	year = {2019},
	pages = {121795},
	abstract = {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{\textendash}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.},
	keywords = {Fokker{\textendash}Planck equation, Languages, Master equation, Rank dynamics},
	issn = {0378-4371},
	doi = {10.1016/j.physa.2019.121795},
	url = {https://doi.org/10.1016/j.physa.2019.121795},
	author = {Germinal Cocho and Rosal{\'\i}o F. Rodr{\'\i}guez and Sergio S{\'a}nchez and Jorge Flores and Carlos Pineda and Carlos Gershenson}
}
