Strict monotonicity of critical points in independent long-range percolation models
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914124215091200 |
|---|---|
| author | Bethuelsen, Stein Andreas Mönch, Christian |
| author_facet | Bethuelsen, Stein Andreas Mönch, Christian |
| contents | We consider independent long-range percolation models on locally finite vertex-transitive graphs. Using coupling ideas we prove strict monotonicity of the critical points with respect to local perturbations in the connection function, thereby improving upon previous results obtained via the classical essential enhancement method of Aizenman and Grimmett in several ways. In particular, our approach allows us to work under minimal assumptions, namely shift-invariance and summability of the connection function, and it applies to both undirected and directed bond percolation models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26314 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strict monotonicity of critical points in independent long-range percolation models Bethuelsen, Stein Andreas Mönch, Christian Probability Mathematical Physics Combinatorics 60K35 (Primary), 82B43 (Secondary) We consider independent long-range percolation models on locally finite vertex-transitive graphs. Using coupling ideas we prove strict monotonicity of the critical points with respect to local perturbations in the connection function, thereby improving upon previous results obtained via the classical essential enhancement method of Aizenman and Grimmett in several ways. In particular, our approach allows us to work under minimal assumptions, namely shift-invariance and summability of the connection function, and it applies to both undirected and directed bond percolation models. |
| title | Strict monotonicity of critical points in independent long-range percolation models |
| topic | Probability Mathematical Physics Combinatorics 60K35 (Primary), 82B43 (Secondary) |
| url | https://arxiv.org/abs/2510.26314 |