Stochastic Modeling of References and Citations

Abstract

We discuss here how the authors compose reference lists of their papers. We assume that the author chooses his references basing on the copying/recursive search algorithm. We put this algorithm at the core of the quantitative model accounting for the age composition of the reference lists of papers. The model contains two empirical functions: the aging function and the obsolescence function, and one empirical parameter—paper’s fitness. At the next step, we calibrate this model in measurements with Physics papers, namely, we determine the aging function, obsolescence function, and paper’s fitness averaged over the groups of similar papers. At the next step, we extend our approach to individual papers and formulate a probabilistic model of their citation dynamics. This model represents citation dynamic of a paper as a self-exciting stochastic process (Hawkes process). We demonstrate that the mean-field approximation of this probabilistic model yields the age distribution of references, as expected.