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arXiv · 2103.16306

Respondent Driven Sampling on sparse Erd\"os-R\'enyi graphs

Anthony Cousien·Jean-Stéphane Dhersin·Viet Chi Tran·Thi Phuong Thuy Vo
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Abstract

We study the exploration of an Erd\"os-R\'enyi 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 Erd\"os-R\'enyi 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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Anthony Cousien, Jean-Stéphane Dhersin, Viet Chi Tran, Thi Phuong Thuy Vo. 2021-03-30. Respondent Driven Sampling on sparse Erd\"os-R\'enyi graphs. https://arxiv.org/abs/2103.16306

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