Ergodicity of PCA: equivalence between spatial and temporal mixing conditions
- For a general attractive Probabilistic Cellular Automata on SZd, we prove that the (time-) convergence towards equilibrium of this Markovian parallel dynamics exponentially fast in the uniform norm is equivalent to a condition (A). This condition means the exponential decay of the influence from the boundary for the invariant measures of the system restricted to finite boxes. For a class of reversible PCA dynamics on {;1, +1}Zd, with a naturally associated Gibbsian potential ;, we prove that a (spatial-) weak mixing condition (WM) for ; implies the validity of the assumption (A); thus exponential (time-) ergodicity of these dynamics towards the unique Gibbs measure associated to ; holds. On some particular examples we state that exponential ergodicity holds as soon as there is no phase transition.
| Verfasserangaben: | Pierre-Yves Louis |
|---|---|
| URL: | http://www.math.washington.edu/%7Eejpecp/ECP/viewarticle.php?id=1704&layout=abstract |
| Publikationstyp: | Wissenschaftlicher Artikel |
| Sprache: | Englisch |
| Jahr der Erstveröffentlichung: | 2004 |
| Erscheinungsjahr: | 2004 |
| Datum der Freischaltung: | 24.03.2017 |
| Quelle: | Electronic Communications in Probability. - 9 (2004), S. 119 - 131 |
| Organisationseinheiten: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| Peer Review: | Nicht referiert |
