论文标题
通过持续同源性的固定点过程的自相似演变
The self-similar evolution of stationary point processes via persistent homology
论文作者
论文摘要
持续的同源性提供了一种强大的方法，可以从点云数据推断拓扑结构。在这里，我们探讨了嵌入到概率环境中的点云的持续同源性，从而利用了点过程理论。我们介绍了有关持续图的空间的衡量标准以及其中的单参数家族的自相似缩放。作为主要结果，我们证明了发生的缩放指数之间的包装关系。
Persistent homology provides a robust methodology to infer topological structures from point cloud data. Here we explore the persistent homology of point clouds embedded into a probabilistic setting, exploiting the theory of point processes. We introduce measures on the space of persistence diagrams and the self-similar scaling of a one-parameter family of these. As the main result we prove a packing relation between the occurring scaling exponents.
