2015/09/22 by Crane, Harry
#FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1509.06701
The transition law of every exchangeable Feller process on the space of countable graphs is determined by a σ-finite measure on the space of \0,1\×\0,1\-valued arrays. In discrete-time, this characterization amounts to a construction from an independent, identically distributed sequence of exchangeable random functions. In continuous-time, the behavior is enriched by a Lévy--Itô-type decomposition of the jump measure into mutually singular components that govern global, vertex-level, and edge-level dynamics. Furthermore, every such process almost surely projects to a Feller process in the space of graph limits.