Persistent Betti numbers of random \v{C}ech complexes
Algebraic Topology
2018-01-26 v1 Computational Geometry
Metric Geometry
Abstract
We study the persistent homology of random \v{C}ech complexes. Generalizing a method of Penrose for studying random geometric graphs, we first describe an appropriate theoretical framework in which we can state and address our main questions. Then we define the kth persistent Betti number of a random \v{C}ech complex and determine its asymptotic order in the subcritical regime. This extends a result of Kahle on the asymptotic order of the ordinary kth Betti number of such complexes to the persistent setting.
Keywords
Cite
@article{arxiv.1801.08376,
title = {Persistent Betti numbers of random \v{C}ech complexes},
author = {Ulrich Bauer and Florian Pausinger},
journal= {arXiv preprint arXiv:1801.08376},
year = {2018}
}
Comments
11 pages, 1 figure