A large-deviations principle for all the components in a sparse inhomogeneous random graph

@article{Andreis2021ALP,
  title={A large-deviations principle for all the components in a sparse inhomogeneous random graph},
  author={Luisa Andreis and Wolfgang K{\"o}nig and H. T. Langhammer and Robert I. A. Patterson},
  journal={Probability Theory and Related Fields},
  year={2021}
}
We study an inhomogeneous sparse random graph, $${\mathcal G }_N$$ G N , on $$[N]=\{1,\dots ,N\}$$ [ N ] = { 1 , ⋯ , N } as introduced in a seminal paper by Bollobás et al. (Random Struct Algorithms 31(1):3–122, 2007): vertices have a type (here in a compact metric space $${\mathcal S }$$ S ), and edges between different vertices occur randomly and independently over all vertex pairs, with a probability depending on the two vertex types. In the limit $$N\rightarrow… 

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