A simple method for finite range decomposition of quadratic forms and Gaussian fields

摘要

We present a simple method to decompose the Green forms corresponding to alarge class of interesting symmetric Dirichlet forms into integrals oversymmetric positive semi-definite and finite range (properly supported) formsthat are smoother than the original Green form. This result gives rise tomultiscale decompositions of the associated Gaussian free fields into sums ofindependent smoother Gaussian fields with spatially localized correlations. Ourmethod makes use of the finite propagation speed of the wave equation andChebyshev polynomials. It improves several existing results and also givessimpler proofs.