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Recentering with Malliavin derivative

Yvain Bruned, Aurélien Minguella

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.

Recentering with Malliavin derivative

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.
Paper Structure (5 sections, 5 theorems, 26 equations)

This paper contains 5 sections, 5 theorems, 26 equations.

Table of Contents

  1. Introduction
  2. Decorated trees and recentering map
  3. Characterisations of the recentering map
  4. Derivative approach
  5. Recursive definition

Key Result

theorem 1

The algebraic parts of the convergence proofs via the spectral gap inequality in LOTHS23BH23 rely on a recentering map $\mathrm{d}\Gamma$ whose expression on decorated trees is given by (dGamma)

Theorems & Definitions (13)

  • theorem 1
  • definition 1
  • definition 2
  • definition 3
  • definition 4
  • lemma 1
  • proof
  • theorem 2
  • proof
  • proposition 1
  • ...and 3 more