The alliterations have fat tails

Several quite different phenomena distribute according to few different functions, which share in a gross sense a particular shape that has induced to call them “fat (heavy, long) tail distributions”. Well-known examples are the so-called Benford’s law, Bradford’s law, Heap’s law, Lotka’s law, and so on. In economics are well known Lorenz’s law and Pareto’s law (on inequality of incoming). In psycholinguistics the most celebrated is undoubtedly Zipf’s law. In this study, we have investigated in this light the alliterations, that is, the relationship between the number of words interposed between two words sharing the same letter at the beginning (x) and number of occurrences of each given x, that is n(x). Analysing different excerpts of texts of XIX Century of different authors (Italian, French and American novelists like D’Annunzio, France and James, or essayists like Leopardi), we found invariably an excellent fit to Lorenz’s law, with an always above .97, and a remarkable stability of parameters within each author, but not between them. However, the mechanisms, which generate such distributions, are far to be clearly understood.