A top-down approach to algebraic renormalization in regularity structures based on multi-indices
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866916375953408000 |
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| author | Bruned, Yvain Linares, Pablo |
| author_facet | Bruned, Yvain Linares, Pablo |
| contents | We provide an algebraic framework to describe renormalization in regularity structures based on multi-indices for a large class of semi-linear stochastic PDEs. This framework is ``top-down", in the sense that we postulate the form of the counterterm and use the renormalized equation to build a canonical smooth model for it. The core of the construction is a generalization of the Hopf algebra of derivations in [LOT23], which is extended beyond the structure group to describe the model equation via an exponential map: This allows to implement a renormalization procedure which resembles the preparation map approach in our context. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_03036 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A top-down approach to algebraic renormalization in regularity structures based on multi-indices Bruned, Yvain Linares, Pablo Probability Analysis of PDEs Rings and Algebras 60H17, 60L30, 60L70 We provide an algebraic framework to describe renormalization in regularity structures based on multi-indices for a large class of semi-linear stochastic PDEs. This framework is ``top-down", in the sense that we postulate the form of the counterterm and use the renormalized equation to build a canonical smooth model for it. The core of the construction is a generalization of the Hopf algebra of derivations in [LOT23], which is extended beyond the structure group to describe the model equation via an exponential map: This allows to implement a renormalization procedure which resembles the preparation map approach in our context. |
| title | A top-down approach to algebraic renormalization in regularity structures based on multi-indices |
| topic | Probability Analysis of PDEs Rings and Algebras 60H17, 60L30, 60L70 |
| url | https://arxiv.org/abs/2307.03036 |