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Large deviations for empirical measures of generalized random graphs

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  • Qun Liu
  • Zhishan Dong

Abstract

In a generalized random graph with random vertex weights, we investigate the asymptotic behaviors for two crucial empirical measures: The empirical pair measure, which represents the number of edges connecting each pair of weights, and the empirical neighborhood measure, which interprets the number of vertices of a given weight connected to a given number of vertices of each weight. By some mixing approaches, we obtain the large deviation principles for these empirical measures in the weak topology. Through these large deviation results, the large deviation principle for the number of edges in a generalized random graph is obtained, as well as the large deviation principle for the empirical degree distribution.

Suggested Citation

  • Qun Liu & Zhishan Dong, 2022. "Large deviations for empirical measures of generalized random graphs," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(8), pages 2676-2687, April.
    • Handle: RePEc:taf:lstaxx:v:51:y:2022:i:8:p:2676-2687
    DOI: 10.1080/03610926.2020.1779748
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