Nodal Volumes as Differentiable Functionals of Gaussian fields
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914778310508544 |
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| author | Peccati, Giovanni Stecconi, Michele |
| author_facet | Peccati, Giovanni Stecconi, Michele |
| contents | We characterize the absolute continuity of the law and the Malliavin-Sobolev regularity of random nodal volumes associated with smooth Gaussian fields on generic $\mathcal{C}^2$ manifolds with arbitrary dimension. Our results extend and generalize the seminal contribution by Angst and Poly (2020) about stationary fields on Euclidean spaces and cover, in particular, the case of two-dimensional manifolds, possibly with boundary and corners. The main tools exploited in the proofs include the use of Gaussian measures on Banach spaces, Morse theory, and the characterization of Malliavin-Sobolev spaces in terms of ray absolute continuity. Several examples are analyzed in detail. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_20243 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nodal Volumes as Differentiable Functionals of Gaussian fields Peccati, Giovanni Stecconi, Michele Probability Differential Geometry 60G15, 60H07, 60G60, 58K05, 28A75 We characterize the absolute continuity of the law and the Malliavin-Sobolev regularity of random nodal volumes associated with smooth Gaussian fields on generic $\mathcal{C}^2$ manifolds with arbitrary dimension. Our results extend and generalize the seminal contribution by Angst and Poly (2020) about stationary fields on Euclidean spaces and cover, in particular, the case of two-dimensional manifolds, possibly with boundary and corners. The main tools exploited in the proofs include the use of Gaussian measures on Banach spaces, Morse theory, and the characterization of Malliavin-Sobolev spaces in terms of ray absolute continuity. Several examples are analyzed in detail. |
| title | Nodal Volumes as Differentiable Functionals of Gaussian fields |
| topic | Probability Differential Geometry 60G15, 60H07, 60G60, 58K05, 28A75 |
| url | https://arxiv.org/abs/2403.20243 |