有向构形网络的排序算法
Ranking algorithms on directed configuration networks
摘要：
本文研究了一个家庭的排名，其中包括谷歌的PageRank，在一个有向配置模型的分布。特别是，它示出的随机选择的节点在图中的秩的分布收敛于分布到一个有限的随机变量$\mathcal{R}^*$，可以被写为一个线性组合的i.i.d.形式为$$\mathcal{R} \stackrel{\mathcal{D}}{=} \sum_{i=1}^{\mathcal{N}} \mathcal{C}_i \mathcal{R}_i + \mathcal{Q},$$的随机不动点方程的内生解的副本，其中$(\mathcal{Q}, \mathcal{N}, \{ \mathcal{C}_i\})$是具有$\mathcal{N} \in \{0,1,2,\dots\}$、$P(|\mathcal{Q}| > 0) > 0$的实值向量，并且$\{\mathcal{R}_i\}$是i.i.d. $\mathcal{R}$的拷贝，独立于$(\mathcal{Q}, \mathcal{N}, \{ \mathcal{C}_i\})$。此外，我们提供了精确的渐近极限$\mathcal{R}^*$，当在度分布的有向配置模型的幂律意味着幂律分布的$\mathcal{R}^*$具有相同的指数。
英文摘要：
This paper studies the distribution of a family of rankings, which includes Google's PageRank, on a directed configuration model. In particular, it is shown that the distribution of the rank of a randomly chosen node in the graph converges in distribution to a finite random variable $\mathcal{R}^*$ that can be written as a linear combination of i.i.d. copies of the endogenous solution to a stochastic fixed point equation of the form $$\mathcal{R} \stackrel{\mathcal{D}}{=} \sum_{i=1}^{\mathcal{N}} \mathcal{C}_i \mathcal{R}_i + \mathcal{Q},$$ where $(\mathcal{Q}, \mathcal{N}, \{ \mathcal{C}_i\})$ is a real-valued vector with $\mathcal{N} \in \{0,1,2,\dots\}$, $P(|\mathcal{Q}| > 0) > 0$, and the $\{\mathcal{R}_i\}$ are i.i.d. copies of $\mathcal{R}$, independent of $(\mathcal{Q}, \mathcal{N}, \{ \mathcal{C}_i\})$. Moreover, we provide precise asymptotics for the limit $\mathcal{R}^*$, which when the in-degree distribution in the directed configuration model has a power law imply a power law distribution for $\mathcal{R}^*$ with the same exponent.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
