Symmetries for the gKPZ equation via multi-indices
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910252690046976 |
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| author | Bellingeri, Carlo Bruned, Yvain |
| author_facet | Bellingeri, Carlo Bruned, Yvain |
| contents | In this work, we study the two main symmetries for the one-dimensional generalised KPZ equation (gKPZ): the chain rule and the Itô Isometry. We consider the equation in the full-subcritical regimes and use multi-indices that avoid an over-parametrization of the renormalised equation to compute the dimension of the two spaces associated with these two symmetries. Our proof is quite elementary and shows that multi-indices provide in this case a simplification in comparison to the results obtained via decorated trees. It also completes the program on the study of the chain rule initiated in arxiv:1902.02884 and continued in arxiv:2403.17066. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_00834 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symmetries for the gKPZ equation via multi-indices Bellingeri, Carlo Bruned, Yvain Probability Analysis of PDEs Rings and Algebras In this work, we study the two main symmetries for the one-dimensional generalised KPZ equation (gKPZ): the chain rule and the Itô Isometry. We consider the equation in the full-subcritical regimes and use multi-indices that avoid an over-parametrization of the renormalised equation to compute the dimension of the two spaces associated with these two symmetries. Our proof is quite elementary and shows that multi-indices provide in this case a simplification in comparison to the results obtained via decorated trees. It also completes the program on the study of the chain rule initiated in arxiv:1902.02884 and continued in arxiv:2403.17066. |
| title | Symmetries for the gKPZ equation via multi-indices |
| topic | Probability Analysis of PDEs Rings and Algebras |
| url | https://arxiv.org/abs/2410.00834 |