# 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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