Exponential phi-mixing implies exponential psi-mixing for Markov fields on bounded degree graphs
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914154104750080 |
|---|---|
| author | Zimmermann, Elias |
| author_facet | Zimmermann, Elias |
| contents | We show that for non-degenerate $k$-Markovian random fields with finite state space over a bounded degree graph with exponential growth rate $θ$ uniform $ϕ$-mixing with exponential decay rate $λ> 3θ$ implies uniform $ψ$-mixing with exponential decay rate $(λ- 3θ)/9$. As an application we obtain exponential $ψ$-mixing for Gibbs fields on regular trees arising from finite range potentials such as the Ising model at low inverse temperature or the Potts model with sufficiently many spin states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09692 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exponential phi-mixing implies exponential psi-mixing for Markov fields on bounded degree graphs Zimmermann, Elias Probability We show that for non-degenerate $k$-Markovian random fields with finite state space over a bounded degree graph with exponential growth rate $θ$ uniform $ϕ$-mixing with exponential decay rate $λ> 3θ$ implies uniform $ψ$-mixing with exponential decay rate $(λ- 3θ)/9$. As an application we obtain exponential $ψ$-mixing for Gibbs fields on regular trees arising from finite range potentials such as the Ising model at low inverse temperature or the Potts model with sufficiently many spin states. |
| title | Exponential phi-mixing implies exponential psi-mixing for Markov fields on bounded degree graphs |
| topic | Probability |
| url | https://arxiv.org/abs/2511.09692 |