Singularity of solutions to singular SPDEs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911412489551872 |
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| author | Hairer, Martin Kusuoka, Seiichiro Nagoji, Hirotatsu |
| author_facet | Hairer, Martin Kusuoka, Seiichiro Nagoji, Hirotatsu |
| contents | Building on the notes [Hai17], we give a sufficient condition for the marginal distribution of the solution of singular SPDEs on the $d$-dimensional torus to be singular with respect to the law of the Gaussian measure induced by the linearised equation. As applications we obtain the singularity of the $Φ^4_3$-measure with respect to the Gaussian free field measure and the border of parameters for the fractional $Φ^4$-measure to be singular with respect to the Gaussian free field measure. Our approach is applicable to quite a large class of singular SPDEs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10037 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Singularity of solutions to singular SPDEs Hairer, Martin Kusuoka, Seiichiro Nagoji, Hirotatsu Probability 60H15, 60H17 Building on the notes [Hai17], we give a sufficient condition for the marginal distribution of the solution of singular SPDEs on the $d$-dimensional torus to be singular with respect to the law of the Gaussian measure induced by the linearised equation. As applications we obtain the singularity of the $Φ^4_3$-measure with respect to the Gaussian free field measure and the border of parameters for the fractional $Φ^4$-measure to be singular with respect to the Gaussian free field measure. Our approach is applicable to quite a large class of singular SPDEs. |
| title | Singularity of solutions to singular SPDEs |
| topic | Probability 60H15, 60H17 |
| url | https://arxiv.org/abs/2409.10037 |