Attractive regular stochastic chains: perfect simulation and phase transition

Details Attractive regular stochastic chains: perfect simulation and phase transition Attractive regular stochastic chains: perfect simulation and phase transition

2011-10-29

arxiv.org/abs/1110.6530v1

Mathematics

Probability

22 pages, 1 pseudo-algorithm

Scientific paper

We prove that uniqueness of the stationary chain compatible with an attractive regular probability kernel is equivalent to the following two assertions for this chain: (1) it is a finitary coding of an i.i.d. process with discrete state space, (2) the concentration of measure holds at exponential rate. We show in particular that if a stationary chain is uniquely defined by a kernel which is continuous and attractive, then this chain can be sampled using a coupling-from-the-past algorithm. For the original Bramson-Kalikow model we further prove that there exists a unique compatible chain if and only if the chain is a finitary coding of a finite alphabet i.i.d. process. Finally, we obtain some partial results on conditions for phase transition for general chains of infinite order.

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