The Annals of Applied Probability

Kalikow-type decomposition for multicolor infinite range particle systems

A. Galves, N. L. Garcia, E. Löcherbach, and E. Orlandi

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

First available in Project Euclid: 21 June 2013

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Primary: 60J25: Continuous-time Markov processes on general state spaces 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82B20: Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs

Interacting particle systems infinite range interactions continuous spin systems perfect simulation random Markov chains Kalikow-type decomposition


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.

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