Phase transition for a non-attractive infection process in heterogeneous environment
- We consider a non-attractive three state contact process on Z and prove that there exists a regime of survival as well as a regime of extinction. In more detail, the process can be regarded as an infection process in a dynamic environment, where non-infected sites are either healthy or passive. Infected sites can recover only if they have a healthy site nearby, whereas non-infected sites may become infected only if there is no healthy and at least one infected site nearby. The transition probabilities are governed by a global parameter q: for large q, the infection dies out, and for small enough q, we observe its survival. The result is obtained by a coupling to a discrete time Markov chain, using its drift properties in the respective regimes.
| Author: | Marinus Gottschau, Markus HeydenreichORCiDGND, Kilian Matzke, Cristina Toninelli |
|---|---|
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/103790 |
| Parent Title (English): | arxiv |
| Publisher: | arXiv |
| Type: | Preprint |
| Language: | English |
| Date of Publication (online): | 2023/04/20 |
| Year of first Publication: | 2017 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2023/04/24 |
| Issue: | arXiv:1706.08216 |
| DOI: | https://doi.org/10.48550/arXiv.1706.08216 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Stochastik und ihre Anwendungen |
