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Acta Mathematica Sinica, English Series

, Volume 34, Issue 10, pp 1626–1634 | Cite as

Large Deviations in Generalized Random Graphs with Node Weights

  • Qun Liu
  • Zhi Shan Dong
Article
  • 6 Downloads

Abstract

Generalized random graphs are considered where the presence or absence of an edge depends on the weights of its nodes. Our main interest is to investigate large deviations for the number of edges per node in such a generalized random graph, where the node weights are deterministic under some regularity conditions, as well as chosen i.i.d. from a finite set with positive components. When the node weights are random variables, obstacles arise because the independence among edges no longer exists, our main tools are some results of large deviations for mixtures. After calculating, our results show that the corresponding rate functions for the deterministic case and the random case are very different.

Keywords

Large deviations mixture generalized random graphs 

MR(2010) Subject Classification

05C80 60F10 

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Notes

Acknowledgements

We thank the referees for their time and comments.

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematics School and Institute of Jilin UniversityChangchunP. R. China

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