The Annals of Applied Probability

Dense graph limits under respondent-driven sampling

Siva Athreya and Adrian Röllin

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1472745456

Digital Object Identifier
doi:10.1214/15-AAP1144

Mathematical Reviews number (MathSciNet)
MR3543894

Zentralblatt MATH identifier
1350.05151

Subjects
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

Keywords
Random graph dense graph limits ergodic respondent driven sampling

Citation

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. https://projecteuclid.org/euclid.aoap/1472745456


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