Scaling limits for fractional polyharmonic Gaussian fields

This work is concerned with fractional Gaussian fields, i.e. Gaussian fields whose covariance operator is given by the inverse fractional Laplacian \((-\Delta)^{-s}\) (where, in particular, we include the case \(s >1\)). We define a lattice discretization of these fields and show that their scaling limits -- with respect to the optimal Besov space topology (up to an endpoint case) -- are the original continuous fields. As a byproduct, in dimension \(d