Perfect simulation and finitary coding for multicolor systems with interactions of infinite range

Details Perfect simulation and finitary coding for multicolor systems with interactions of infinite range Perfect simulation and finitary coding for multicolor systems with interactions of infinite range

2008-09-20

arxiv.org/abs/0809.3494v3

Mathematics

Probability

Scientific paper

We consider a particle system on $Z^d$ with finite state space and interactions of infinite range. Assuming that the rate of change is continuous and decays sufficiently fast, we introduce a perfect simulation algorithm for the stationary process. The algorithm follows from a representation of the multicolor system as a finitary coding from a sequence of independent uniform random variables. This implies that the process is exponentially ergodic. The basic tool we use is a representation of the infinite range change rates as a mixture of finite range change rates.

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