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Strong couplings for static locally tree-like random graphs

Part of: Markov processes Graph theory

Published online by Cambridge University Press:  11 November 2022

Mariana Olvera-Cravioto Open the ORCID record for Mariana Olvera-Cravioto [Opens in a new window]
Mariana Olvera-Cravioto*
Affiliation:
University of North Carolina at Chapel Hill
*
*Postal address: Department of Statistics and Operations Research, University of North Carolina, Chapel HIll. Email: [email protected]
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Abstract

We provide a general purpose result for the coupling of exploration processes of random graphs, both undirected and directed, with their local weak limits when this limit is a marked Galton–Watson process. This class includes in particular the configuration model and the family of inhomogeneous random graphs with rank-1 kernel. Vertices in the graph are allowed to have attributes on a general separable metric space and can potentially influence the construction of the graph itself. The coupling holds for any fixed depth of a breadth-first exploration process.

Keywords

Random graphscomplex networksGalton–Watson processesconfiguration modelinhomogeneous random graphlocal-weak limits

MSC classification

Primary: 05C80: Random graphs
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 05C82: Small world graphs, complex networks
Type
Original Article
Information
Journal of Applied Probability , Volume 59 , Issue 4 , December 2022 , pp. 1261 - 1285
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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