Note on down-set thresholds
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914803552878592 |
|---|---|
| author | Warnke, Lutz |
| author_facet | Warnke, Lutz |
| contents | Gunby-He-Narayanan showed that the logarithmic gap predictions of Kahn-Kalai and Talagrand (proved by Park-Pham and Frankston-Kahn-Narayanan-Park) about thresholds of up-sets do not apply to down-sets. In particular, for the down-set of triangle-free graphs, they showed that there is a polynomial gap between the threshold and the factional expectation threshold. In this short note we give a simpler proof of this result, and extend the polynomial threshold gap to down-sets of F-free graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_11662 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Note on down-set thresholds Warnke, Lutz Probability Combinatorics 60C05, 05D40, 05C80 Gunby-He-Narayanan showed that the logarithmic gap predictions of Kahn-Kalai and Talagrand (proved by Park-Pham and Frankston-Kahn-Narayanan-Park) about thresholds of up-sets do not apply to down-sets. In particular, for the down-set of triangle-free graphs, they showed that there is a polynomial gap between the threshold and the factional expectation threshold. In this short note we give a simpler proof of this result, and extend the polynomial threshold gap to down-sets of F-free graphs. |
| title | Note on down-set thresholds |
| topic | Probability Combinatorics 60C05, 05D40, 05C80 |
| url | https://arxiv.org/abs/2310.11662 |