Random Geometric Complexes

@article{Kahle2011RandomGC,
  title={Random Geometric Complexes},
  author={Matthew Kahle},
  journal={Discrete \& Computational Geometry},
  year={2011},
  volume={45},
  pages={553-573}
}
  • Matthew Kahle
  • Published 2011
  • Mathematics, Computer Science
  • Discrete & Computational Geometry
We study the expected topological properties of Čech and Vietoris–Rips complexes built on random points in ℝd. We find higher-dimensional analogues of known results for connectivity and component counts for random geometric graphs. However, higher homology Hk is not monotone when k>0.In particular, for every k>0, we exhibit two thresholds, one where homology passes from vanishing to nonvanishing, and another where it passes back to vanishing. We give asymptotic formulas for the expectation of… Expand
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On the vanishing of homology in random Čech complexes
Limit theorems for Betti numbers of random simplicial complexes
The Morse theory of Čech and Delaunay complexes
On the topology of random complexes built over stationary point processes.
Homological Connectivity in Random Čech Complexes
Random Chain Complexes
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