For sufficiently small ε, the stationary Gaussian Markov random field on Z^d is an explicit factor of an i.i.d. process and admits finitely dependent approximations with exponential total variation decay.
Maximal Branching Processes and ’Long-Range Percolation’.Journal of Applied Probability, 7(1):89–98
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Glauber dynamics and coupling-from-the-past for Gaussian fields
For sufficiently small ε, the stationary Gaussian Markov random field on Z^d is an explicit factor of an i.i.d. process and admits finitely dependent approximations with exponential total variation decay.