Name
Abstract | ||
|---|---|---|
We consider k-dimensional random simplicial complexes generated from the binomial random (k + 1)-uniform hypergraph by taking the downward-closure. For 1 <= j <= k - 1, we determine when all cohomology groups with coefficients in F2 from dimension one up to j vanish and the zero-th cohomology group is isomorphic to F2. This property is not deterministically monotone for this model, but nevertheless we show that it has a single sharp threshold. Moreover we prove a hitting time result, relating the vanishing of these cohomology groups to the disappearance of the last minimal obstruction. We also study the asymptotic distribution of the dimension of the j-th cohomology group inside the critical window. As a corollary, we deduce a hitting time result for a different model of random simplicial complexes introduced by Linial and Meshulam, previously only known for dimension two. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1002/rsa.20857 | RANDOM STRUCTURES & ALGORITHMS |
Keywords | Field | DocType |
connectedness,hitting time,random hypergraphs,random simplicial complexes,sharp threshold | Combinatorics,Cohomology,Mathematics | Journal |
Volume | Issue | ISSN |
56.0 | 2.0 | 1042-9832 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Oliver Cooley | 1 | 39 | 9.15 |
| Nicola Del Giudice | 2 | 0 | 0.34 |
| Mihyun Kang | 3 | 163 | 29.18 |
| Philipp Sprüssel | 4 | 0 | 0.34 |