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Soft random simplicial complexes
- Publication Year :
- 2023
-
Abstract
- A soft random graph $G(n,r,p)$ can be obtained from the random geometric graph $G(n,r)$ by keeping every edge in $G(n,r)$ with probability $p$. This random graph is a particular case of the soft random graph model introduced by Penrose, in which the probability between 2 vertices is a function that depends on the distance between them. In this article, we define models for random simplicial complexes built over the soft random graph $G(n,r,p)$, which also present randomness in all other dimensions. Furthermore, we study the homology of those random simplicial complexes in different regimes of $n,r$, and $p$ by giving asymptotic formulas for the expectation of the Betti numbers in the sparser regimes, and bounds in the denser regimes.<br />Comment: 20 pages. arXiv admin note: text overlap with arXiv:2311.10625
- Subjects :
- Mathematics - Algebraic Topology
Mathematics - Combinatorics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2311.13034
- Document Type :
- Working Paper