We investigate the joint distribution of nodes of small degrees and the degree profile in preferential dynamic attachment circuits. In particular, we study the joint asymptotic distribution of the number of the nodes of outdegree 0 (terminal nodes) and outdegree 1 in a very large circuit. The expectation and variance of the number of those two types of nodes are both asymptotically linear with respect to the age of the circuit. We show that the numbers of nodes of outdegree 0 and 1 asymptotically follow a two-dimensional Gaussian law via multivariate martingale methods. The rate of convergence is derived analytically. We also study the exact distribution of the degree of a node, as the circuit ages, via a series of Pólya-Eggenberger urn models with “hiccups” in between. The exact expectation and variance of the degree of nodes are determined by recurrence methods. Phase transitions of these degrees are discussed briefly. This is an extension of the abstract (Zhang 2016).

中文翻译：

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优先动态附加电路中的小度数和度数分布的节点。

我们研究了优先度动态附着电路中小度节点的联合分布和度分布。特别是，我们研究了一个非常大的电路中0度（终端节点）和1度的节点数目的联合渐近分布。相对于电路寿命，这两种类型的节点数量的期望和方差都呈渐近线性。我们显示，通过多元mar方法，0度和1度外节点的数目渐近遵循二维高斯定律。收敛速度是通过分析得出的。我们还通过一系列带有“打ic”的Pólya-Eggenberger缸模型研究了随着电路老化，节点度的确切分布。节点程度的确切期望和方差是通过递归方法确定的。简要讨论了这些度数的相变。这是摘要的扩展（Zhang 2016）。