Kalikow-type decomposition for multicolor infinite range particle systems

TL;DR

This paper introduces a Kalikow-type decomposition for infinite-range particle systems with continuous change rates, enabling perfect simulation and explicit coupling construction under high noise conditions.

Contribution

It provides a novel decomposition method for infinite-range interactions and develops a perfect simulation algorithm for stationary distributions.

Findings

Decomposition of infinite-range rates into finite-range mixtures

Feasible perfect simulation algorithm under high noise

Explicit coupling construction for Ornstein's ar-distance

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.