Abstract
The transition law of every exchangeable Feller process on the space of countable graphs is determined by a \(\sigma \)-finite measure on the space of \(\{0,1\}\times \{0,1\}\)-valued arrays. In discrete time, this characterization gives rise to a construction from an independent, identically distributed sequence of exchangeable random functions. In continuous time, the behavior is enriched by a Lévy–Itô–Khintchine-type decomposition of the jump measure into mutually singular components that govern global, vertex-level, and edge-level dynamics. Every such process almost surely projects to a Feller process in the space of graph limits.
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Crane, H. Exchangeable graph-valued Feller processes. Probab. Theory Relat. Fields 168, 849–899 (2017). https://doi.org/10.1007/s00440-016-0726-0
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DOI: https://doi.org/10.1007/s00440-016-0726-0
Keywords
- Exchangeability
- Random graph
- Graph limit
- Lévy–Itô–Khintchine decomposition
- Aldous–Hoover theorem
- Erdős–Rényi random graph
Mathematics Subject Classification
- 05C80
- 60G09
- 60J05
- 60J25