Ergodicity of PCA
- For a general attractive Probabilistic Cellular Automata on S-Zd, 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), wit a naturally associated Gibbsian potential rho, we prove that a (spatial-) weak mixing condition (WM) for rho implies the validity of the assumption (A); thus exponential (time-) ergodicity of these dynamics towards the unique Gibbs measure associated to rho hods. On some particular examples we state that exponential ergodicity holds as soon as there is no phase transition.
| Verfasserangaben: | Pierre-Yves Louis |
|---|---|
| URN: | urn:nbn:de:kobv:517-opus-6589 |
| Untertitel (Englisch): | equivalence between spatial and temporal mixing conditions |
| Publikationstyp: | Postprint |
| Sprache: | Englisch |
| Erscheinungsjahr: | 2004 |
| Veröffentlichende Institution: | Universität Potsdam |
| Datum der Freischaltung: | 20.03.2006 |
| Freies Schlagwort / Tag: | Stochastische Zellulare Automaten; Wechselwirkende Teilchensysteme ERgodicity of Markov Chains; Gibbs measures; Interacting particle systems; Probabilistic Cellular Automata |
| GND-Schlagwort: | Wahrscheinlichkeitstheorie |
| Quelle: | ELECTRONIC COMMUNICATIONS IN PROBABILITY. - ISSN 1083-589X . - 9 (2004), S. 119 - 131 |
| Organisationseinheiten: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC-Klassifikation: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Externe Anmerkung: | AMS 2000 Subject classification: 60G60 , 60J10 , 60K35 , 82C20 , 82C26 , 37B15 first published at: Electronic Communications in Probability, 9 (2004) paper 13, pages 119-131 |
