Topology of random geometric complexes: a survey

Omer Bobrowski; Matthew Kahle

doi:10.1007/s41468-017-0010-0

Topology of random geometric complexes: a survey

Omer Bobrowski, Matthew Kahle

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	331-364
Number of pages	34
Journal	Journal of Applied and Computational Topology
Volume	1
Issue number	3-4
DOIs	https://doi.org/10.1007/s41468-017-0010-0
State	Published - Jun 2018

Keywords

Boolean model
Homology
Random graphs
Random topology
Simplicial complexes

All Science Journal Classification (ASJC) codes

Applied Mathematics
Computational Mathematics
Geometry and Topology

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10.1007/s41468-017-0010-0

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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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AB - 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.

KW - Boolean model

KW - Homology

KW - Random graphs

KW - Random topology

KW - Simplicial complexes

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M3 - مقالة

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JF - Journal of Applied and Computational Topology

IS - 3-4

ER -

Topology of random geometric complexes: a survey

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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