A characterisation of the continuum Gaussian free field in $d \geq 2$ dimensions
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866910460647833600 |
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| author | Aru, Juhan Powell, Ellen |
| author_facet | Aru, Juhan Powell, Ellen |
| contents | We prove that under certain mild moment and continuity assumptions, the $d$-dimensional Gaussian free field is the only stochastic process in $d\geq 2$ that is translation invariant, exhibits a certain scaling, and satisfies the usual domain Markov property. Our proof is based on a decomposition of the underlying functional space in terms of radial processes and spherical harmonics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_07273 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A characterisation of the continuum Gaussian free field in $d \geq 2$ dimensions Aru, Juhan Powell, Ellen Probability 60G15, 60G60, 60J65 We prove that under certain mild moment and continuity assumptions, the $d$-dimensional Gaussian free field is the only stochastic process in $d\geq 2$ that is translation invariant, exhibits a certain scaling, and satisfies the usual domain Markov property. Our proof is based on a decomposition of the underlying functional space in terms of radial processes and spherical harmonics. |
| title | A characterisation of the continuum Gaussian free field in $d \geq 2$ dimensions |
| topic | Probability 60G15, 60G60, 60J65 |
| url | https://arxiv.org/abs/2103.07273 |