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Local probabilities of randomly stopped sums of power-law lattice random variables
Lithuanian Mathematical Journal ( IF 0.5 ) Pub Date : 2019-10-01 , DOI: 10.1007/s10986-019-09462-9
Mindaugas Bloznelis

Let $X_1$ and $N$ be non-negative integer valued power law random variables. For a randomly stopped sum $S_N=X_1+\cdots+X_N$ of independent and identically distributed copies of $X_1$ we establish a first order asymptotics of the local probabilities $P(S_N=t)$ as $t\to+\infty$. Using this result we show the $k^{-\delta}$, $0\le \delta\le 1$ scaling of the local clustering coefficient (of a randomly selected vertex of degree $k$) in a power law affiliation network.

中文翻译:

随机停止的幂律格随机变量总和的局部概率

让 $X_1$ 和 $N$ 是非负整数值的幂律随机变量。对于 $X_1$ 的独立同分布副本的随机停止和 $S_N=X_1+\cdots+X_N$,我们建立局部概率 $P(S_N=t)$ 的一阶渐近式为 $t\to+\infty$ . 使用这个结果,我们展示了幂律附属网络中局部聚类系数(随机选择的度数为 $k$ 的顶点)的 $k^{-\delta}$, $0\le \delta\le 1$ 缩放。
更新日期:2019-10-01
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