Renormalised Models for Variable Coefficient Singular SPDEs
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908442148470784 |
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| author | Broux, Lucas Singh, Harprit Steele, Rhys |
| author_facet | Broux, Lucas Singh, Harprit Steele, Rhys |
| contents | In this work we prove convergence of renormalised models in the framework of regularity structures [Hai14] for a wide class of variable coefficient singular SPDEs in their full subcritical regimes. In particular, we provide for the first time an extension of the main results of [CH16, HS24, BH23] beyond the translation invariant setting. In the non-translation invariant setting, it is necessary to introduce renormalisation functions rather than renormalisation constants. We show that under a very general assumption, which we prove covers the case of second order parabolic operators, these renormalisation functions can be chosen to be local in the sense that their space-time dependence enters only through a finite order jet of the coefficient field of the differential operator at the given space-time point. Furthermore we show that the models we construct depend continuously on the coefficient field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06851 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Renormalised Models for Variable Coefficient Singular SPDEs Broux, Lucas Singh, Harprit Steele, Rhys Analysis of PDEs Functional Analysis Probability In this work we prove convergence of renormalised models in the framework of regularity structures [Hai14] for a wide class of variable coefficient singular SPDEs in their full subcritical regimes. In particular, we provide for the first time an extension of the main results of [CH16, HS24, BH23] beyond the translation invariant setting. In the non-translation invariant setting, it is necessary to introduce renormalisation functions rather than renormalisation constants. We show that under a very general assumption, which we prove covers the case of second order parabolic operators, these renormalisation functions can be chosen to be local in the sense that their space-time dependence enters only through a finite order jet of the coefficient field of the differential operator at the given space-time point. Furthermore we show that the models we construct depend continuously on the coefficient field. |
| title | Renormalised Models for Variable Coefficient Singular SPDEs |
| topic | Analysis of PDEs Functional Analysis Probability |
| url | https://arxiv.org/abs/2507.06851 |