A rough path perspective on renormalization
We revisit (higher-order) translation operators on rough paths, in both the geometric and branched setting. As in Hairer's work on the renormalization of singular SPDEs we propose a purely algebraic view on the matter. Recent advances in the theory of regularity structures, especially the Hopf...
| Hoofdauteurs: | , , , |
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| Formaat: | Journal article |
| Gepubliceerd in: |
Elsevier
2019
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| Samenvatting: | We revisit (higher-order) translation operators on rough paths, in both the geometric and branched setting. As in Hairer's work on the renormalization of singular SPDEs we propose a purely algebraic view on the matter. Recent advances in the theory of regularity structures, especially the Hopf algebraic interplay of positive and negative renormalization of Bruned--Hairer--Zambotti (2016), are seen to have precise counterparts in the rough path context, even with a similar formalism (short of polynomial decorations and colourings). Renormalization is then seen to correspond precisely to (higher-order) rough path translation. |
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