Topology of random geometric complexes: a survey

2014/09/16 by Bobrowski, Omer, Kahle, Matthew · 8 citations
#05E45. Secondary: 55U10 #60D05 #Algebraic Topology (math.AT) #FOS: Mathematics #Metric Geometry (math.MG) #Primary: 60B99 #Probability (math.PR)

paper · doi:10.48550/arxiv.1409.4734

Abstract

In this expository article, we survey the rapidly emerging area of random geometric simplicial complexes.

Cited by

• Total 2-cut complexes of powers of cycle graphs and Cartesian products of certain graphs
• Persistent reachability homology in machine learning applications
• Universal topological statistics on triangulated singular spaces
• Covariance matrices of volume power functionals of random simplicial complexes -- an asymptotic analysis
• Modeling Non-Uniform Hypergraphs Using Determinantal Point Processes
• Using dense graph limit theory to count cocycles of random simplicial complexes
• Hybrid quantum-classical framework for Betti number estimation with applications to topological data analysis
• Cycle-Consistent Helmholtz Machine: Goal-Seeded Simulation via Inverted Inference

Related

• Topology of random simplicial complexes: a survey
• Random simplicial complexes
• Random Simplicial Complexes
• Large random simplicial complexes, I
• Soft random simplicial complexes