Glauber dynamics and coupling-from-the-past for Gaussian fields
Dynamique de Glauber et couplage par le passé pour champs Gaussiens
Résumé
In this paper, we study a centered Gaussian field on Z^d defined by the following: the conditional law of the field at any site i ∈ Z^d is Gaussian of mean ε times the mean of the neighbours, and of variance 1. We show that when ε is small enough, this model can be written as a factor of an i.i.d. process, and that it is exponentially close to a finitely dependent model. Furthermore, if the field is conditioned to take values in a compact, we show that the factor can be realised with exponential tails.
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