The paper establishes sampling convergence of the configuration model, preferential attachment model, generalized random graph, and bipartite configuration model to graphexes, giving necessary and sufficient conditions for convergence.
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Pith papers citing it
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math.PR 2years
2019 2verdicts
UNVERDICTED 2representative citing papers
The paper corrects Kallenberg's theorem by adding a missing condition for local finiteness of jointly exchangeable random measures and provides a counterexample showing the original statement is incomplete.
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Limits of Sparse Configuration Models and Beyond: Graphexes and Multi-Graphexes
The paper establishes sampling convergence of the configuration model, preferential attachment model, generalized random graph, and bipartite configuration model to graphexes, giving necessary and sufficient conditions for convergence.
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A correction to Kallenberg's theorem for jointly exchangeable random measures
The paper corrects Kallenberg's theorem by adding a missing condition for local finiteness of jointly exchangeable random measures and provides a counterexample showing the original statement is incomplete.