## Asymptotics for isotropic Hilbert-valued spherical random fields

In this talk, we introduce the concept of isotropic Hilbert-valued spherical random field, thus extending the notion of isotropic spherical random field to an infinite-dimensional setting. We then establish a spectral representation theorem and a functional Schoenberg’s theorem. Following some key results established for the real-valued case, we prove consistency and quantitative central limit theorem for the sample power spectrum operators in the high-frequency regime.

Area: CS47 - Statistical inference in infinite-dimensional spaces (Alessia Caponera)

Keywords: spherical random fields, Hilbert spaces, isotropy, spectral represen- tation, high-frequency asymptotics, quantitative central limit theorem

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