Abstract
We prove some exponential Chebyshev inequality and derive the large deviation principle and the law of large numbers for the graphons constructed from a sequence of Erdős–Rényi random graphs with weights. Also, we obtain a new version of the large deviation principle for the number of triangles included in an Erdős–Rényi graph.
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Funding
The authors were partially supported by the Russian Science Foundation (Grant 18–11–00129).
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Logachov, A.V., Mogulskii, A.A. Exponential Chebyshev Inequalities for Random Graphons and Their Applications. Sib Math J 61, 697–714 (2020). https://doi.org/10.1134/S0037446620040114
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DOI: https://doi.org/10.1134/S0037446620040114