Theory of Probability &Its Applications, Volume 66, Issue 3, Page 376-390, January 2021.
We consider the model of an $N$-vertex configuration graph where the number of edges is at most $n$ and the degrees of vertices are independent and identically distributed (i.i.d.) random variables (r.v.'s). The distribution of the r.v. $\xi$, which is defined as the degree of any given vertex, is assumed to satisfy the condition $p_k=\mathbf{P}\{\xi=k\}\sim\frac{L}{k^g\ln^h k}$ as $k\to\infty$, where $L>0$, $g>1$, $h\ge0$. Limit theorems for the number of vertices of a given degree as $N, n\to\infty$ are proved.

中文翻译：

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边数有界的配置图中给定度的顶点数的极限分布

Theory of Probability & Its Applications，第 66 卷，第 3 期，第 376-390 页，2021 年 1 月。
我们考虑 $N$-顶点配置图的模型，其中边数最多为 $n$，顶点度数为独立同分布 (iid) 随机变量 (rv's)。定义为任何给定顶点的度数的 rv $\xi$ 的分布假设满足条件 $p_k=\mathbf{P}\{\xi=k\}\sim\frac{L} {k^g\ln^hk}$ 为 $k\to\infty$，其中 $L>0$，$g>1$，$h\ge0$。证明了给定度的顶点数为$N，n\to\infty$的极限定理。