Topology of random geometric complexes: a survey

In 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 p...

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Bibliographic Details
Published inJournal of applied and computational topology Vol. 1; no. 3-4; pp. 331 - 364
Main Authors Bobrowski, Omer, Kahle, Matthew
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2018
Subjects
Algebraic Topology
Computational Science and Engineering
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Boolean model
60D05
Random graphs
Random topology
Secondary 55U10
Homology
Simplicial complexes
Primary 60B99
05E45
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Summary:In 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 the probabilistic behavior of the homology (and related structures) generated by these random complexes.
ISSN:2367-1726
2367-1734
DOI:10.1007/s41468-017-0010-0