Exponential Decay of Correlations for the Strongly Coupled Toom Model

Details Exponential Decay of Correlations for the Strongly Coupled Toom Model Exponential Decay of Correlations for the Strongly Coupled Toom Model

2011-10-07

arxiv.org/abs/1110.1540v1

Physics

Mathematical Physics

17 pages, 0 figure, submitted to J. Stat. Phys

Scientific paper

We prove that, for the two-dimensional probabilistic cellular automaton of
Toom in the low-noise regime, there are two classes of initial measures, each
of which converges exponentially fast toward one of the two natural invariant
measures. We also show that these two invariant measures have exponential decay
of correlations in space and in time and are strongly mixing.

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