Diffusion approximation of a network model of meme popularity

Models of meme propagation on social networks, in which memes compete for limited user attention, can successfully reproduce the heavy-tailed popularity distributions observed online settings. While system-wide have been derived analytically, dynamics individual trajectories thus far evaded description. To address this, we formulate diffusion a given as one-dimensional stochastic process, whose fluctuations result from aggregating local network using classic and generalized central limit theorems, with latter based stable distribution theory. Ultimately, our approach decouples competing popularities, allowing them to be simulated independently, parallelized expressed terms Fokker-Planck equations.