Isomorphisms between random $d$-hypergraphs
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909195022893056 |
|---|---|
| author | Lenoir, Théo |
| author_facet | Lenoir, Théo |
| contents | We characterize the size of the largest common induced subgraph of two independent random uniform $d$-hypergraphs of different sizes with $d\geq 3$. More precisely, its distribution is asymptotically concentrated on two points, and we obtain as a consequence a phase transition for the inclusion of the smallest hypergraph in the largest one. This generalizes to uniform random $d$-hypergraphs the results of Chatterjee and Diaconis for uniform random graphs.
Our proofs rely on the first and second moment methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04670 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Isomorphisms between random $d$-hypergraphs Lenoir, Théo Combinatorics Probability 60C05, 05C80, 05C65 We characterize the size of the largest common induced subgraph of two independent random uniform $d$-hypergraphs of different sizes with $d\geq 3$. More precisely, its distribution is asymptotically concentrated on two points, and we obtain as a consequence a phase transition for the inclusion of the smallest hypergraph in the largest one. This generalizes to uniform random $d$-hypergraphs the results of Chatterjee and Diaconis for uniform random graphs. Our proofs rely on the first and second moment methods. |
| title | Isomorphisms between random $d$-hypergraphs |
| topic | Combinatorics Probability 60C05, 05C80, 05C65 |
| url | https://arxiv.org/abs/2405.04670 |