Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.11963 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911269170184192 |
|---|---|
| author | Velasco, Sonia |
| author_facet | Velasco, Sonia |
| contents | We introduce an interacting particle system which models the inherited sterility method. Individuals evolve on $\mathbb{Z}^d$ according to a contact process with parameter $λ>0$. With probability $p \in [0,1]$ an offspring is fertile and can give birth to other individuals at rate $λ$. With probability $1-p$, an offspring is sterile and blocks the site it sits on until it dies. The goal is to prove that at fixed $λ$, the system survives for large enough $p$ and dies out for small enough $p$. The model is not attractive, since an increase of fertile individuals potentially causes that of sterile ones. However, thanks to a comparison argument with attractive models, we are able to answer our question. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11963 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extinction and survival in inherited sterility Velasco, Sonia Probability We introduce an interacting particle system which models the inherited sterility method. Individuals evolve on $\mathbb{Z}^d$ according to a contact process with parameter $λ>0$. With probability $p \in [0,1]$ an offspring is fertile and can give birth to other individuals at rate $λ$. With probability $1-p$, an offspring is sterile and blocks the site it sits on until it dies. The goal is to prove that at fixed $λ$, the system survives for large enough $p$ and dies out for small enough $p$. The model is not attractive, since an increase of fertile individuals potentially causes that of sterile ones. However, thanks to a comparison argument with attractive models, we are able to answer our question. |
| title | Extinction and survival in inherited sterility |
| topic | Probability |
| url | https://arxiv.org/abs/2404.11963 |