2021/03/30 by Anthony Cousien, Jean-Stéphane Dhersin, Cousien, Anthony +5
Mathematics · #05C80 #05C81 #60F17 #60J20 #62D05 #FOS: Mathematics #G.2.2 #G.3 #Probability (math.PR) #acm:05C80 #acm:05C81 #acm:60F17 #acm:60J20 #acm:62D05 #math.PR #msc:05C80 #msc:05C81 #msc:60F17 #msc:60J20 #msc:62D05
paper · pdf · doi:10.48550/arxiv.2103.16306
31 pages, 6 figures
arxiv created 2021/03/30 · arxiv updated 2021/03/31
We study the exploration of an Erdös-Rényi random graph by a respondent-driven sampling method, where discovered vertices reveal their neighbours. Some of them receive coupons to reveal in their turn their own neighbourhood. 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.