Convex order and faster transmission in first contact percolation
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917540723163136 |
|---|---|
| author | Jahnel, Benedikt Köppl, Jonas Lüchtrath, Lukas Vu, Anh Duc |
| author_facet | Jahnel, Benedikt Köppl, Jonas Lüchtrath, Lukas Vu, Anh Duc |
| contents | Inspired by strict-monotonicity criteria for the time constant in first passage percolation, we investigate convex ordering of point processes in relation to the time constant in first contact percolation. In a nutshell, first contact percolation models the spread of an infection as a contact process without recovery based on a generalized graphical representation, where the usual homogeneous Poisson point processes on the edges are replaced by general simple point processes. Based on a notion of convex ordering for point processes, we prove monotonicity in the number and existence of infection paths. We argue that this convex ordering is however not enough to ensure strict monotonicities in the asymptotic speed of the infection. Instead, we propose a criterion based on an ordering of void probabilities and prove a speed-up for one-dimensional systems based on $\mathbb{Z}$-stationary point processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28766 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convex order and faster transmission in first contact percolation Jahnel, Benedikt Köppl, Jonas Lüchtrath, Lukas Vu, Anh Duc Probability Mathematical Physics Primary 60K35, Secondary 60G55 Inspired by strict-monotonicity criteria for the time constant in first passage percolation, we investigate convex ordering of point processes in relation to the time constant in first contact percolation. In a nutshell, first contact percolation models the spread of an infection as a contact process without recovery based on a generalized graphical representation, where the usual homogeneous Poisson point processes on the edges are replaced by general simple point processes. Based on a notion of convex ordering for point processes, we prove monotonicity in the number and existence of infection paths. We argue that this convex ordering is however not enough to ensure strict monotonicities in the asymptotic speed of the infection. Instead, we propose a criterion based on an ordering of void probabilities and prove a speed-up for one-dimensional systems based on $\mathbb{Z}$-stationary point processes. |
| title | Convex order and faster transmission in first contact percolation |
| topic | Probability Mathematical Physics Primary 60K35, Secondary 60G55 |
| url | https://arxiv.org/abs/2605.28766 |