论文标题
移动双曲线图中检测时间的尾部界限
Tail bounds for detection times in mobile hyperbolic graphs
论文作者
论文摘要
由Krioukov等人的真实世界网络的随机双曲线图模型的动机，并受到Peres等人对Euclidean Space中图形动态模型的分析的启发，我们介绍了荷滑图的动态模型，该模型可以根据棕色动作维持Vertice Invertice Invertice Invertice Invertice Invertice inthybolic Space Invertice hyphybolic Spectics hyphybolic Spectics hyphybolic Spectiant的动态模型。对于角度和径向运动速度的不同参数，我们分析尾部边界以检测固定目标的检测时间，并获得完全不同的状态，即检测到目标的方式和何时检测到的完整图片：作为通过时间的函数，我们表征了粒子通常检测到目标的粒子的子集的子集。 我们克服了欧几里得空间中不存在的几个实质性技术困难，并在尾部范围内提供了完整的图像。在途中，我们还获得了更通用的连续过程的新结果，随着漂移和在某些地区花费的障碍，我们还获得了改进的界限，以实现帕累托随机变量的独立总和。
Motivated by Krioukov et al.'s model of random hyperbolic graphs for real-world networks, and inspired by the analysis of a dynamic model of graphs in Euclidean space by Peres et al., we introduce a dynamic model of hyperbolic graphs in which vertices are allowed to move according to a Brownian motion maintaining the distribution of vertices in hyperbolic space invariant. For different parameters of the speed of angular and radial motion, we analyze tail bounds for detection times of a fixed target and obtain a complete picture, for very different regimes, of how and when the target is detected: as a function of the time passed, we characterize the subset of the hyperbolic space where particles typically detecting the target are initially located. We overcome several substantial technical difficulties not present in Euclidean space, and provide a complete picture on tail bounds. On the way, we obtain also new results for the time more general continuous processes with drift and reflecting barrier spent in certain regions, and we also obtain improved bounds for independent sums of Pareto random variables.
