## The Annals of Applied Probability

### Kalikow-type decomposition for multicolor infinite range particle systems

#### Abstract

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.

#### Article information

Source
Ann. Appl. Probab., Volume 23, Number 4 (2013), 1629-1659.

Dates
First available in Project Euclid: 21 June 2013

https://projecteuclid.org/euclid.aoap/1371834040

Digital Object Identifier
doi:10.1214/12-AAP882

Mathematical Reviews number (MathSciNet)
MR3098444

Zentralblatt MATH identifier
1281.60079

#### Citation

Galves, A.; Garcia, N. L.; Löcherbach, E.; Orlandi, E. Kalikow-type decomposition for multicolor infinite range particle systems. Ann. Appl. Probab. 23 (2013), no. 4, 1629--1659. doi:10.1214/12-AAP882. https://projecteuclid.org/euclid.aoap/1371834040

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