论文标题
持续循环和孔的极端寿命
Extremal life times of persistent loops and holes
论文作者
论文摘要
持续的同源性捕获了拓扑特征的外观和消失，例如循环和孔时，以泊松点过程为中心。我们研究了在有限组成部分和出生resp中死亡的特征的寿命时代的极端价值。死亡时间远离连续渗透的阈值。首先，我们描述了一般特征维度的最小寿命时间的缩放以及Čech综合体中孔的最大寿命时间的缩放时间。然后，我们进行了更精致的分析，并建立了泊松近似，以弥漫的寿命和小寿命时期。最后，我们还研究了在越野河流环境中最小寿命的缩放，并指出了与čech综合体的令人惊讶的差异。
Persistent homology captures the appearances and disappearances of topological features such as loops and holes when growing disks centered at a Poisson point process. We study extreme values for the life times of features dying in bounded components and with birth resp. death time bounded away from the threshold for continuum percolation. First, we describe the scaling of the minimal life times for general feature dimensions, and of the maximal life times for holes in the Čech complex. Then, we proceed to a more refined analysis and establish Poisson approximation for large life times of holes and for small life times of loops. Finally, we also study the scaling of minimal life times in the Vietoris-Rips setting and point to a surprising difference to the Čech complex.
