# 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}
}
• Published 25 November 2021
• Mathematics, Computer Science
• Probability Theory and Related Fields
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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• Mathematics
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