随机因子标度扇形图最大顶点度的聚焦
Focusing of Maximum Vertex Degrees in Random Faulty Scaled Sector Graphs
摘要：
本文研究了具有随机顶点和边故障的二项/泊松随机标度扇形图的最大出度/入度的性质。我们证明了概率分布的最大程度的随机故障缩放扇区图的$n$顶点，其中每个顶点跨越一个部门的$α$弧度，半径$r_n\ll \sqrt{\ln n/n}$，成为集中在两个连续的整数，故障概率的一些自然的假设。
英文摘要：
In this paper we study the behavior of maximum out/in-degree of binomial/Poisson random scaled sector graphs in the presence of random vertex and edge faults. We prove that the probability distribution of maximum degrees for random faulty scaled sector graphs with $n$ vertices, where each vertex spans a sector of $α$ radians, with radius $r_n\ll \sqrt{\ln n/n}$, become concentrated on two consecutive integers, under some natural assumptions of faulty probabilities.
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