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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2024, Volume 21, Issue 2, Pages 914–926
DOI: https://doi.org/10.33048/semi.2024.21.060 (Mi semr1723) 		 
Probability theory and mathematical statistics

Note on normal approximation for number of triangles in heterogeneous Erdős-Rényi graph

A. V. Logachovab, A. A. Mogulskiia, A. A. Yambartsevc

a Lab. of Probability Theory and Math. Statistics, Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
b Dep. of Computer Science in Economics, Novosibirsk State Technical University pr. K. Marksa, 20, 630073, Novosibirsk, Russia
c Institute of Mathematics and Statistics, University of São Paulo, Rua do Matão, 1010, CEP o5508-090, São Paulo, SP, Brazil
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DOI: https://doi.org/10.33048/semi.2024.21.060
Abstract: We obtain a bound for the convergence rate in the central limit theorem for the number of triangles in a heterogeneous Erdős-Rényi graphs. Our approach is reminiscent of Hoeffding decomposition (a common technique in the theory of U-statistics). We show that the centered and normalized number of triangles asymptotically behaves as the normalized sum of centered independent random variables when the number of vertices increases. The proposed method is simple and intuitive.
Keywords: Erdős-Rényi random graphs, central limit theorem, large deviations principle.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-281
FWNF-2022-0010
Fundação de Amparo à Pesquisa do Estado de São Paulo 2022/01030-0
2017/10555-0
Logachov A.V. thanks Mathematical Center in Akademgorodok under the agreement N. 075-15-2022-281 with the Ministry of Science and Higher Education of the Russian Federation; Mogulskii A.A. is supported by the Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0010; Logachov A.V., Yambartsev A.A. thanks FAPESP grant 2022/01030-0; Yambartsev A.A. thanks FAPESP grant 2017/10555-0
Received March 7, 2024, published November 1, 2024
Document Type: Article
UDC: 519.21
MSC: 05C80, 60F05, 60F10
Language: English
Citation: A. V. Logachov, A. A. Mogulskii, A. A. Yambartsev, “Note on normal approximation for number of triangles in heterogeneous Erdős-Rényi graph”, Sib. Èlektron. Mat. Izv., 21:2 (2024), 914–926
Citation in format AMSBIB
\Bibitem{LogMogYam24}
\by A.~V.~Logachov, A.~A.~Mogulskii, A.~A.~Yambartsev
\paper Note on normal approximation for number of triangles in heterogeneous Erd\H{o}s-R\'enyi graph
\jour Sib. \`Elektron. Mat. Izv.
\yr 2024
\vol 21
\issue 2
\pages 914--926
\mathnet{http://mi.mathnet.ru/semr1723}
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