Recentering with Malliavin derivative

TL;DR

This paper unifies spectral gap proofs for the convergence of renormalized models in regularity structures by algebraically characterizing the recentering map used in the process.

Contribution

It offers an algebraic framework that unifies and characterizes the recentering map in spectral gap proofs for regularity structures.

Findings

Recentered models are characterized algebraically.

Spectral gap proofs are unified through this algebraic approach.

The recentering map is given via equivalent characterizations.

Abstract

We provide an algebraic unification of the spectral gap proofs of the convergence of the renormalised model for regularity structures. We show that the key recentering map used in the literature for adjusting the recentering of the model is given via equivalent characterisations.