Electronic Communications in Probability

Respondent-Driven Sampling and Sparse Graph Convergence

Siva Athreya and Adrian Röllin

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We consider a particular respondent-driven sampling procedure governed by a graphon. Using a specific clumping procedure of the sampled vertices, we construct a sequence of sparse graphs. If the sequence of the vertex-sets is stationary, then the sequence of sparse graphs converges to the governing graphon in the cut-metric. The tools used are a concentration inequality for Markov chains and the Stein-Chen method.

Article information

Electron. Commun. Probab., Volume 23 (2018), paper no. 3, 12 pp.

Received: 9 May 2017
Accepted: 4 December 2017
First available in Project Euclid: 3 February 2018

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Zentralblatt MATH identifier

Primary: 05C80: Random graphs [See also 60B20]
Secondary: 37A30: Ergodic theorems, spectral theory, Markov operators {For operator ergodic theory, see mainly 47A35}

Respondent-driven sampling random graph sparse-graph limits dense graph limits

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Athreya, Siva; Röllin, Adrian. Respondent-Driven Sampling and Sparse Graph Convergence. Electron. Commun. Probab. 23 (2018), paper no. 3, 12 pp. doi:10.1214/17-ECP103. https://projecteuclid.org/euclid.ecp/1517626933

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