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Respondent-driven sampling on sparse Erdös-Rényi graphs

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-03183146
Contributor : Thi Phuong Thuy Vo <>
Submitted on : Friday, March 26, 2021 - 11:21:38 PM
Last modification on : Friday, April 2, 2021 - 3:20:56 AM

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  • HAL Id : hal-03183146, version 1

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Anthony Cousien, Jean-Stéphane Dhersin, Viet Chi Tran, Thi Phuong Thuy Vo. Respondent-driven sampling on sparse Erdös-Rényi graphs. 2021. ⟨hal-03183146⟩

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