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Topology of random geometric complexes: a survey

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Abstract

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.

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Authors and Affiliations

  1. Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel

    Omer Bobrowski

  2. Department of Mathematics, The Ohio State University, Columbus, OH, USA

    Matthew Kahle

Authors
  1. Omer Bobrowski
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  2. Matthew Kahle
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Correspondence to Omer Bobrowski.

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On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Matthew Kahle gratefully acknowledges support from NSF-DMS #1352386.

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Bobrowski, O., Kahle, M. Topology of random geometric complexes: a survey. J Appl. and Comput. Topology 1, 331–364 (2018). https://doi.org/10.1007/s41468-017-0010-0

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