599
2004
eng
postprint
0
2006-03-20
--
--
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
600
2005
eng
postprint
1
2006-03-20
--
--
Increasing coupling for probabilistic cellular automata
We give a necessary and sufficient condition for the existence of an increasing coupling of N (N >= 2) synchronous dynamics on S-Zd (PCA). Increasing means the coupling preserves stochastic ordering. We first present our main construction theorem in the case where S is totally ordered; applications to attractive PCAs are given. When S is only partially ordered, we show on two examples that a coupling of more than two synchronous dynamics may not exist. We also prove an extension of our main result for a particular class of partially ordered spaces.
urn:nbn:de:kobv:517-opus-6593
659
Statistics & probability letters. - ISSN 0167-7152. - 74 (2005), 1, S. 1 - 13
<hr>2000 MSC: 60K35 , 60E15 , 60J10, 82C20 , 37B15 , 68W10<br><br>first published at:<br><a href="http://dx.doi.org/10.1016/j.spl.2005.04.021" target="_blank">Statistics & Probability Letters, Volume 74, Issue 1 , 1 August 2005, Pages 1-13 </a>
louis@math.uni-potsdam.de + 03319771276
Pierre-Yves Louis
deu
swd
Wahrscheinlichkeitstheorie
deu
uncontrolled
stochastische Anordnung
deu
uncontrolled
stochastische Zellulare Automaten
deu
uncontrolled
Kopplung
eng
uncontrolled
stochastic ordering
eng
uncontrolled
Probabilistic Cellular Automata
eng
uncontrolled
monotone coupling
Mathematik
open_access
Institut für Mathematik
Universität Potsdam
https://publishup.uni-potsdam.de/files/600/louis02.pdf