Geometric embedding for Regularity Structures

Yvain Bruned, Foivos Katsetsiadis

Published 2023-01-14Version 1

In this paper, we show how one can view certain models in Regularity Structures as some form of geometric rough paths. This is performed by identifying the deformed Butcher-Connes-Kreimer Hopf algebra with a quotient of the shuffle Hopf algebra which is the structure underlying the definition of a geometric rough path. This provides an extension of the isomorphism between the Butcher-Connes-Kreimer Hopf algebra and the shuffle Hopf algebra. This new algebraic result relies strongly on the deformation formalism and the post-Lie structures introduced recently in the context of Regularity Structures.