Name
Abstract | ||
|---|---|---|
We consider a generalised model of a random simplicial complex, which arises from a random hypergraph. Our model is generated by taking the downward-closure of a nonuniform binomial random hypergraph, in which for each k, each set of k + 1 vertices forms an edge with some probability p(k) independently. As a special case, this contains an extensively studied model of a (uniform) random simplicial complex, introduced by Meshulam and Wallach [Random Structures & Algorithms 34 (2009), no. 3, pp. 408-417]. We consider a higher-dimensional notion of connectedness on this new model according to the vanishing of cohomology groups over an arbitrary abelian group R. We prove that this notion of connectedness displays a phase transition and determine the threshold. We also prove a hitting time result for a natural process interpretation, in which simplices and their downward-closure are added one by one. In addition, we determine the asymptotic behaviour of cohomology groups inside the critical window around the time of the phase transition. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.37236/10607 | ELECTRONIC JOURNAL OF COMBINATORICS |
DocType | Volume | Issue |
Journal | 29 | 3 |
ISSN | Citations | PageRank |
1077-8926 | 0 | 0.34 |
References | Authors | |
0 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Cooley Oliver | 1 | 0 | 0.34 |
| Del Giudice Nicola | 2 | 0 | 0.34 |
| Mihyun Kang | 3 | 163 | 29.18 |
| Sprüssel Philipp | 4 | 0 | 0.34 |