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Respondent-Driven Sampling on Sparse Erdös-Rényi Graphs
Anthony Cousien
,
Jean-Stéphane Dhersin
,
Viet Chi Tran
,
Thi Phuong Thuy Vo
Abstract
We study the exploration of an Erdös-Rényi 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 Erdös-Rényi 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.