MAXIMALLY PERSISTENT CYCLES IN RANDOM GEOMETRIC COMPLEXES
MAXIMALLY PERSISTENT CYCLES IN RANDOM GEOMETRIC COMPLEXES
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DOI：
10.1214/16-aap1232
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发表时间：
2017-08-01
影响因子：
1.8
通讯作者：
Skraba, Primoz
中科院分区：
文献类型：
--
作者：
Bobrowski, Omer;Kahle, Matthew;Skraba, Primoz
本文首次研究了随机几何单纯复形的持久同调。我们的主要兴趣是在最大持续循环度-k持久的同源性，无论是Cech或Vietoris-Rips过滤建立在一个统一的泊松过程的强度n在单位立方体[0，1]（d）。这是测量随机点集中最大的“k维洞”的自然方法。这个问题是在几何概率和代数拓扑的交叉点上，并且自然地受到拓扑推理的概率观点的启发。
We initiate the study of persistent homology of random geometric simplicial complexes. Our main interest is in maximally persistent cycles of degree-k in persistent homology, for a either the Cech or the Vietoris-Rips filtration built on a uniform Poisson process of intensity n in the unit cube [0, 1](d). This is a natural way of measuring the largest "k-dimensional hole" in a random point set. This problem is in the intersection of geometric probability and algebraic topology, and is naturally motivated by a probabilistic view of topological inference.We show that for all d >= 2 and 1