Open Access
August 2013 Kalikow-type decomposition for multicolor infinite range particle systems
A. Galves, N. L. Garcia, E. Löcherbach, E. Orlandi
Ann. Appl. Probab. 23(4): 1629-1659 (August 2013). DOI: 10.1214/12-AAP882


We consider a particle system on $\mathbb{Z}^{d}$ with real state space and interactions of infinite range. Assuming that the rate of change is continuous we obtain a Kalikow-type decomposition of the infinite range change rates as a mixture of finite range change rates. Furthermore, if a high noise condition holds, as an application of this decomposition, we design a feasible perfect simulation algorithm to sample from the stationary process. Finally, the perfect simulation scheme allows us to forge an algorithm to obtain an explicit construction of a coupling attaining Ornstein’s $\bar{d}$-distance for two ordered Ising probability measures.


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A. Galves. N. L. Garcia. E. Löcherbach. E. Orlandi. "Kalikow-type decomposition for multicolor infinite range particle systems." Ann. Appl. Probab. 23 (4) 1629 - 1659, August 2013.


Published: August 2013
First available in Project Euclid: 21 June 2013

zbMATH: 1281.60079
MathSciNet: MR3098444
Digital Object Identifier: 10.1214/12-AAP882

Primary: 60J25 , 60K35 , 82B20

Keywords: continuous spin systems , infinite range interactions , interacting particle systems , Kalikow-type decomposition , perfect simulation , random Markov chains

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.23 • No. 4 • August 2013
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