599
2004
eng
postprint
0
2006-03-20
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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.
equivalence between spatial and temporal mixing conditions
urn:nbn:de:kobv:517-opus-6589
658
ELECTRONIC COMMUNICATIONS IN PROBABILITY. - ISSN 1083-589X . - 9 (2004), S. 119 - 131
<hr>AMS 2000 Subject classification: 60G60 , 60J10 , 60K35 , 82C20 , 82C26 , 37B15<br><br>first published at:<br><a href="http://www.math.washington.edu/~ejpecp/EcpVol9/paper13.abs.html" target="_blank" >Electronic Communications in Probability, 9 (2004) paper 13, pages 119-131</a>
louis@math.uni-potsdam.de + 03319771276
Pierre-Yves Louis
deu
swd
Wahrscheinlichkeitstheorie
deu
uncontrolled
Wechselwirkende Teilchensysteme
deu
uncontrolled
Stochastische Zellulare Automaten
eng
uncontrolled
Interacting particle systems
eng
uncontrolled
Probabilistic Cellular Automata
eng
uncontrolled
ERgodicity of Markov Chains
eng
uncontrolled
Gibbs measures
Mathematik
open_access
Institut für Mathematik
Universität Potsdam
https://publishup.uni-potsdam.de/files/599/louis01.pdf