Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2510.11424 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911282323521536 |
|---|---|
| author | Bérard, Jean Dembin, Barbara Marêché, Laure |
| author_facet | Bérard, Jean Dembin, Barbara Marêché, Laure |
| contents | We prove a sharpness result for the dynamics of finite-range Interacting Particle Systems (IPS) on $\{0,1\}^{\Z^d}$, which generalizes to a whole class of IPS the sharpness result for the phase transition of the contact process obtained by Bezuidenhout and Grimmett~\cite{BezuidenhoutGrimmett1991}. More precisely, starting from an IPS that is monotone, ergodic, and which admits the all-zero configuration as an absorbing state, we prove that there exists an arbitrarily small perturbation of the dynamics which leads to an \emph{exponentially} ergodic IPS. This also extends the sharpness result previously established for (discrete-time) probabilistic cellular automata in \cite{Har} to the continuous-time setting of IPS. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11424 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharpness for monotone absorbing Interacting Particle Systems Bérard, Jean Dembin, Barbara Marêché, Laure Probability We prove a sharpness result for the dynamics of finite-range Interacting Particle Systems (IPS) on $\{0,1\}^{\Z^d}$, which generalizes to a whole class of IPS the sharpness result for the phase transition of the contact process obtained by Bezuidenhout and Grimmett~\cite{BezuidenhoutGrimmett1991}. More precisely, starting from an IPS that is monotone, ergodic, and which admits the all-zero configuration as an absorbing state, we prove that there exists an arbitrarily small perturbation of the dynamics which leads to an \emph{exponentially} ergodic IPS. This also extends the sharpness result previously established for (discrete-time) probabilistic cellular automata in \cite{Har} to the continuous-time setting of IPS. |
| title | Sharpness for monotone absorbing Interacting Particle Systems |
| topic | Probability |
| url | https://arxiv.org/abs/2510.11424 |