Respondent-Driven Sampling on Sparse Erdös-Rényi Graphs

We study the exploration of an Erdos-Renyi random graph by a respondent-driven sampling method, where discovered vertices reveal their neighbors. Some of them receive coupons to reveal in their turn their own neighborhood. This leads to the study of a Markov chain on the random graph that we study. For sparse Erdos-Renyi graphs of large sizes, this process correctly renormalized converges to the solution of a deterministic curve, solution of a system of ODEs absorbed on the abscissa axis. The associated fluctuation process is also studied, providing a functional central limit theorem, with a Gaussian limiting process. Simulations and numerical computation illustrate the study.