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Pré-Publication, Document De Travail Année : 2021

Respondent-driven sampling on sparse Erdös-Rényi graphs

Résumé

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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Dates et versions

hal-03183146 , version 1 (26-03-2021)
hal-03183146 , version 2 (07-06-2021)

Identifiants

  • 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-03183146v1⟩
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