Topology of random geometric complexes: a survey

@article{Bobrowski2018TopologyOR,
  title={Topology of random geometric complexes: a survey},
  author={O. Bobrowski and M. Kahle},
  journal={Journal of Applied and Computational Topology},
  year={2018},
  volume={1},
  pages={331-364}
}
  • O. Bobrowski, M. Kahle
  • Published 2018
  • Mathematics, Computer Science
  • Journal of Applied and Computational Topology
  • AbstractIn this expository article, we survey the rapidly emerging area of random geometric simplicial complexes. Random geometric complexes may be viewed as higher-dimensional generalizations of random geometric graphs, where vertices are generated by a random point process, and edges are placed based on proximity. Extending the notion of connected components and cycles in graphs, the main object of study has been the homology of these complexes. We review the results known to date about… CONTINUE READING
    69 Citations

    Figures and Topics from this paper.

    Explore Further: Topics Discussed in This Paper

    Random simplicial complexes
    • 5
    • PDF
    22 RANDOM SIMPLICIAL COMPLEXES
    Dynamical Models for Random Simplicial Complexes.
    • 3
    • PDF
    On the subgraphs of percolated random geometric graphs and the associated random complexes
    Homological Connectivity in Random Čech Complexes
    • 5
    • PDF
    On the vanishing of homology in random Čech complexes
    • 23
    • PDF
    Random Chain Complexes
    • 2
    • PDF

    References

    SHOWING 1-10 OF 63 REFERENCES
    Statistics of geometric random simplicial complexes
    • 3
    Random Geometric Complexes
    • M. Kahle
    • Mathematics, Computer Science
    • Discret. Comput. Geom.
    • 2011
    • 119
    • PDF
    Limit theorems for Betti numbers of random simplicial complexes
    • 93
    • PDF
    Random geometric complexes in the thermodynamic regime
    • 53
    • Highly Influential
    • PDF
    Simplicial Homology of Random Configurations
    • 45
    • PDF
    On the vanishing of homology in random Čech complexes
    • 23
    • PDF
    The fundamental group of random 2-complexes
    • 86
    • PDF
    On the topology of random complexes built over stationary point processes.
    • 39
    • Highly Influential
    • PDF
    Topology of random simplicial complexes: a survey
    • 94
    • PDF