144 research outputs found
Geometric embedding for regularity structures
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.Comment: 26 page
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