Finite range decomposition for families of gradient Gaussian measures
  Let a family of gradient Gaussian vector fields on $ \mathbb{Z}^d $ be given. We show the existence of a uniform finite range decomposition of the corresponding covariance operators, that is, the covariance operator can be written as a sum of covariance operators whose kernels are supported within cubes of diameters $ \sim L^k $. In addition we prove natural regularity for the subcovariance operators and we obtain regularity bounds as we vary within the given family of gradient Gaussian measures. 
Stefan Adams and Roman Koteck\'y and Stefan M\"uller
math-ph math.AP math.MP math.PR