Diagram-free approach for convergence of tree-based models in Regularity Structures

In this work, we translate at the level of decorated trees some of the crucial arguments which have been used in arXiv:2112.10739 for proposing a diagram-free approach for the convergence of the model in Regularity Structures. This allows us to broaden the perspective and enlarge the scope of singular SPDEs covered by this approach. It also sheds new light on algebraic structures introduced in the foundational paper of Martin Hairer on Regularity structures which was used later for recursively described renormalised models.Comment: 27 Page