Respondent Driven Sampling on sparse Erd\"os-R\'enyi graphs
Probability
2021-03-31 v1
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.
Keywords
Cite
@article{arxiv.2103.16306,
title = {Respondent Driven Sampling on sparse Erd\"os-R\'enyi graphs},
author = {Anthony Cousien and Jean-Stéphane Dhersin and Viet Chi Tran and Thi Phuong Thuy Vo},
journal= {arXiv preprint arXiv:2103.16306},
year = {2021}
}
Comments
31 pages, 6 figures