Strong couplings for static locally tree-like random graphs
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Published:2022-11-11
Issue:4
Volume:59
Page:1261-1285
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ISSN:0021-9002
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Container-title:Journal of Applied Probability
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language:en
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Short-container-title:J. Appl. Probab.
Author:
Olvera-Cravioto MarianaORCID
Abstract
AbstractWe 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.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability