We give asymptotics for the cumulative distribution function (CDF) for degrees of large dense random graphs sampled from a graphon. The proof is based on precise asymptotics for binomial random variables. This result is a first step for giving a nonparametric test for identifying the degree function of a large random graph. Replacing the indicator function in the empirical CDF by a smoother function, we get general asymptotic results for functionals of homomorphism densities for partially labeled graphs. This general setting allows to recover recent results on asymptotics for homomorphism densities of sampled graphon.

中文翻译：

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从graphon采样的随机图的度和同态密度的累积分布函数的渐近

我们给出了从一个石墨烯采样的大型密集随机图的渐近性的累积分布函数（CDF）的渐近性。该证明基于二项式随机变量的精确渐近性。该结果是提供非参数测试以识别大型随机图的度函数的第一步。用更平滑的函数代替经验CDF中的指标函数，对于部分标记的图，我们得到了同构密度泛函的一般渐近结果。此常规设置允许恢复关于渐近论的最近结果，以获取采样石墨烯的同态密度。