Exponential convergence to equilibrium in supercritical kinetically constrained models at high temperature
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2019
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913437419831296 |
|---|---|
| author | Marêché, Laure |
| author_facet | Marêché, Laure |
| contents | Kinetically constrained models (KCMs) were introduced by physicists to model the liquid-glass transition. They are interacting particle systems on $\mathbb{Z}^d$ in which each element of $\mathbb{Z}^d$ can be in state 0 or 1 and tries to update its state to 0 at rate $q$ and to 1 at rate $1-q$, provided that a constraint is satisfied. In this article, we prove the first non-perturbative result of convergence to equilibrium for KCMs with general constraints: for any KCM in the class termed "supercritical" in dimension 1 and 2, when the initial configuration has product $\mathrm{Bernoulli}(1-q')$ law with $q' \neq q$, the dynamics converges to equilibrium with exponential speed when $q$ is close enough to 1, which corresponds to the high temperature regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1907_05844 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Exponential convergence to equilibrium in supercritical kinetically constrained models at high temperature Marêché, Laure Probability 60K35 Kinetically constrained models (KCMs) were introduced by physicists to model the liquid-glass transition. They are interacting particle systems on $\mathbb{Z}^d$ in which each element of $\mathbb{Z}^d$ can be in state 0 or 1 and tries to update its state to 0 at rate $q$ and to 1 at rate $1-q$, provided that a constraint is satisfied. In this article, we prove the first non-perturbative result of convergence to equilibrium for KCMs with general constraints: for any KCM in the class termed "supercritical" in dimension 1 and 2, when the initial configuration has product $\mathrm{Bernoulli}(1-q')$ law with $q' \neq q$, the dynamics converges to equilibrium with exponential speed when $q$ is close enough to 1, which corresponds to the high temperature regime. |
| title | Exponential convergence to equilibrium in supercritical kinetically constrained models at high temperature |
| topic | Probability 60K35 |
| url | https://arxiv.org/abs/1907.05844 |