Consider an evolving graph where in succeeding time steps new vertices or edges are added by `preferential attachment' — informally, new connections are more likely made with high degree components. In this scheme, which grows a random network, the sequence of degree distributions is an object of interest which sheds light on the evolving structure.

With respect to a type of `nonlinear' preferential attachment, we discuss a fluid limit approach to prove a law of large numbers for the scaled trajectories of the degree distribution, by approximating them in terms of an infinite coupled ODE system. Part of the work relies on analysis of the ODE system in terms of \(C_0\) semigroup methods. Joint work with Jihyeok Choi and Shankar Venkatramani.