Level area of spin random fields: a chaos decomposition
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911051336908800 |
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| author | Pistolato, Francesca Stecconi, Michele |
| author_facet | Pistolato, Francesca Stecconi, Michele |
| contents | We study real left-invariant spin Gaussian fields on $SO(3)$, a special class of non-isotropic random fields used to model the polarization of the Cosmic Microwave Background. Leveraging recent results from "New chaos decomposition of Gaussian nodal volumes" (arXiv:2505.22350), we provide an explicit formula for the Wiener-Itô chaos decomposition of the area measure of level sets of such random fields. Our analysis represents a step forward in the study of second-order asymptotic properties of the Lipschitz-Killing curvatures of excursion sets of spin random fields. Remarkably, our formulas reveal a clear difference between the high frequency regime and the zero spin case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08550 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Level area of spin random fields: a chaos decomposition Pistolato, Francesca Stecconi, Michele Probability Mathematical Physics Differential Geometry 60D05 (Primary) 85A40, 58C35, 42C10 (Secondary) We study real left-invariant spin Gaussian fields on $SO(3)$, a special class of non-isotropic random fields used to model the polarization of the Cosmic Microwave Background. Leveraging recent results from "New chaos decomposition of Gaussian nodal volumes" (arXiv:2505.22350), we provide an explicit formula for the Wiener-Itô chaos decomposition of the area measure of level sets of such random fields. Our analysis represents a step forward in the study of second-order asymptotic properties of the Lipschitz-Killing curvatures of excursion sets of spin random fields. Remarkably, our formulas reveal a clear difference between the high frequency regime and the zero spin case. |
| title | Level area of spin random fields: a chaos decomposition |
| topic | Probability Mathematical Physics Differential Geometry 60D05 (Primary) 85A40, 58C35, 42C10 (Secondary) |
| url | https://arxiv.org/abs/2507.08550 |