2023/01/14 by Bruned, Yvain, Katsetsiadis, Foivos
#Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2301.05896
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.