Universality and variability in the statistics of data with fat-tailed distributions: the case of word frequencies in natural languages

Natural language is a remarkable example of a complex dynamical system which combines variation and universal structure emerging from the interaction of millions of individuals. Understanding statistical properties of texts is not only crucial in applications of information retrieval and natural language processing, e.g. search engines, but also allow deeper insights into the organization of knowledge in the form of written text. In this thesis, we investigate the statistical and dynamical processes underlying the coexistence of universality and variability in word statistics. We combine a careful statistical analysis of large empirical databases on language usage with analytical and numerical studies of stochastic models