Characterizing models in regularity structures

The centered model is a crucial ingredient in the theory of regularity structures, used for a solution theory of singular stochastic PDEs. It provides a parametrization of the solution manifold, of which we seek to get robust control as an artificial smoothing parameter is removed.

In this talk, we will give a robust characterization of the model in regularity structures, which persists for rough noise. We will then show, how this characterization can be used to propagate symmetries from the noise to the model. Furthermore, we show that a convergent sequence of noise ensembles, satisfying uniformly a spectral gap assumption, implies convergence of the associated models. Combined with the characterization, this establishes a universality-type result.