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–Renyi random graphs with weights. Also, we obtain a new version of the large deviation principle for the number of triangles included in an Erdős–Renyi graph.

中文翻译：

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随机图形的指数 Chebyshev 不等式及其应用

我们证明了一些指数 Chebyshev 不等式，并推导出大偏差原理和大数定律，用于从一系列具有权重的 Erdős-Renyi 随机图构建的图子。此外，我们获得了 Erdős-Renyi 图中三角形数量的大偏差原理的新版本。