On the Aldous-Caputo Spectral Gap Conjecture for Hypergraphs
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909742044020736 |
|---|---|
| author | Alon, Gil Kozma, Gady Puder, Doron |
| author_facet | Alon, Gil Kozma, Gady Puder, Doron |
| contents | In their celebrated paper (arXiv:0906.1238), Caputo, Liggett and Richthammer proved Aldous' conjecture and showed that for an arbitrary finite graph, the spectral gap of the interchange process is equal to the spectral gap of the underlying random walk. A crucial ingredient in the proof was the Octopus Inequality - a certain inequality of operators in the group ring $\mathbb{R}[\mathrm{Sym}_n]$ of the symmetric group. Here we generalize the Octopus Inequality and apply it to generalize the Caputo-Liggett-Richthammer Theorem to certain hypergraphs, proving some cases of a conjecture of Caputo. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_02505 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Aldous-Caputo Spectral Gap Conjecture for Hypergraphs Alon, Gil Kozma, Gady Puder, Doron Group Theory Combinatorics Probability Representation Theory 20c30 (Primary) 05c81, 05c65, 20B30, 05c50, 60b15, 60j10, 60k35(Secondary) In their celebrated paper (arXiv:0906.1238), Caputo, Liggett and Richthammer proved Aldous' conjecture and showed that for an arbitrary finite graph, the spectral gap of the interchange process is equal to the spectral gap of the underlying random walk. A crucial ingredient in the proof was the Octopus Inequality - a certain inequality of operators in the group ring $\mathbb{R}[\mathrm{Sym}_n]$ of the symmetric group. Here we generalize the Octopus Inequality and apply it to generalize the Caputo-Liggett-Richthammer Theorem to certain hypergraphs, proving some cases of a conjecture of Caputo. |
| title | On the Aldous-Caputo Spectral Gap Conjecture for Hypergraphs |
| topic | Group Theory Combinatorics Probability Representation Theory 20c30 (Primary) 05c81, 05c65, 20B30, 05c50, 60b15, 60j10, 60k35(Secondary) |
| url | https://arxiv.org/abs/2311.02505 |