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- W4280494738 abstract "For a smooth stationary Gaussian field on $mathbb{R}^d$ and level $ell in mathbb{R}$, we consider the number of connected components of the excursion set ${f ge ell}$ (or level set ${f = ell}$) contained in large domains. The mean of this quantity is known to scale like the volume of the domain under general assumptions on the field. We prove that, assuming sufficient decay of correlations (e.g. the Bargmann-Fock field), a central limit theorem holds with volume-order scaling. Previously such a result had only been established for `additive' geometric functionals of the excursion/level sets (e.g. the volume or Euler characteristic) using Hermite expansions. Our approach, based on a martingale analysis, is more robust and can be generalised to a wider class of topological functionals. A major ingredient in the proof is a third moment bound on critical points, which is of independent interest." @default.
- W4280494738 created "2022-05-22" @default.
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- W4280494738 date "2022-05-18" @default.
- W4280494738 modified "2023-10-14" @default.
- W4280494738 title "A central limit theorem for the number of excursion set components of Gaussian fields" @default.
- W4280494738 doi "https://doi.org/10.48550/arxiv.2205.09085" @default.
- W4280494738 hasPublicationYear "2022" @default.
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