In this talk, we will present the convergence of the renormalised model of the generalised KPZ equation via local transformations that are governed by preparation maps. The main idea is an extension of a result on the convergence of a class Feynman diagrams given by Hairer and Quastel.
With this extension, one is able to perform local transformations that make appear the renormalisation given for a model defined recursively via preparation maps in the context of Regularity Structures. This approach works both in the discrete and continuous settings and could lead to a general convergence theorem.