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.
Citation
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. https://doi.org/10.1214/12-AAP882
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