Gigantic random simplicial complexes

2017/12/02 by Jens Grygierek, Grygierek, Jens, Martina Juhnke-Kubitzke +7 · 1 citation
Mathematics · #55U10 #60D05 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #math.AT #math.CO #math.PR #msc:55U10 #msc:60D05

paper · pdf · doi:10.48550/arxiv.1712.00589

arxiv created 2017/12/02 · arxiv updated 2017/12/05

Abstract

We provide a random simplicial complex by applying standard constructions to a Poisson point process in Euclidean space. It is gigantic in the sense that - up to homotopy equivalence - it almost surely contains infinitely many copies of every compact topological manifold, both in isolation and in percolation.

Cited by

• Covariance matrices of volume power functionals of random simplicial complexes -- an asymptotic analysis

Related

• On the Dimension of Random Simplicial Complexes
• Topology of random geometric complexes: a survey
• Random geometric complexes in the thermodynamic regime
• Maximally Persistent Cycles in Random Geometric Complexes
• Random simplicial complexes