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