The Annals of Applied Probability

Dense graph limits under respondent-driven sampling

Siva Athreya and Adrian Röllin

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We consider certain respondent-driven sampling procedures on dense graphs. We show that if the sequence of the vertex-sets is ergodic then the limiting graph can be expressed in terms of the original dense graph via a transformation related to the invariant measure of the ergodic sequence. For specific sampling procedures, we describe the transformation explicitly.

Article information

Ann. Appl. Probab., Volume 26, Number 4 (2016), 2193-2210.

Received: April 2014
Revised: September 2015
First available in Project Euclid: 1 September 2016

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Zentralblatt MATH identifier

Primary: 05C80: Random graphs [See also 60B20] 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40]
Secondary: 37A30: Ergodic theorems, spectral theory, Markov operators {For operator ergodic theory, see mainly 47A35} 9482

Random graph dense graph limits ergodic respondent driven sampling


Athreya, Siva; Röllin, Adrian. Dense graph limits under respondent-driven sampling. Ann. Appl. Probab. 26 (2016), no. 4, 2193--2210. doi:10.1214/15-AAP1144.

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