Large Deviations in Generalized Random Graphs with Node Weights

Large Deviations in Generalized Random Graphs with Node Weights 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematica Sinica, English Series Springer Journals

Large Deviations in Generalized Random Graphs with Node Weights

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Publisher
Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
Copyright
Copyright © 2018 by 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
Subject
Mathematics; Mathematics, general
ISSN
1439-8516
eISSN
1439-7617
D.O.I.
10.1007/s10114-018-7357-6
Publisher site
See Article on Publisher Site

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.

Journal

Acta Mathematica Sinica, English SeriesSpringer Journals

Published: May 7, 2018

References

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