Perfect simulation and finitary coding for multicolor systems with interactions of infinite range
Probability
2009-04-04 v3
Abstract
We consider a particle system on 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.
Cite
@article{arxiv.0809.3494,
title = {Perfect simulation and finitary coding for multicolor systems with interactions of infinite range},
author = {A. Galves and N. L. Garcia and E. Loecherbach},
journal= {arXiv preprint arXiv:0809.3494},
year = {2009}
}