Level area of spin random fields: a chaos decomposition

2025/07/11 by Pistolato, Francesca, Stecconi, Michele
#42C10 (Secondary) #58C35 #60D05 (Primary) 85A40 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2507.08550

Abstract

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.

Citations

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Related

• Geometry and topology of spin random fields
• Expected Lipschitz-Killing curvatures for spin random fields and other non-isotropic fields
• Limiting Behavior for the Excursion Area of Band-Limited Spherical Random Fields
• New chaos decomposition of Gaussian nodal volumes
• Asymptotic Behaviour of Level Sets of Needlet Random Fields