A Covariance Formula for the Number of Excursion Set Components of Gaussian Fields and Applications

Authors

Dmitry Beliaev, University of OxfordFollow
Michael McAuley, Technological University DublinFollow
Stephen Muirhead, University of MelbourneFollow

Author ORCID Identifier

0000-0003-2486-931X

Document Type

Article

Disciplines

1.1 MATHEMATICS

Publication Details

https://www.semanticscholar.org/paper/A-covariance-formula-for-the-number-of-excursion-of-Beliaev-McAuley/f67a40d87893e934f8b0b01e7f7a3f1d0425add9

doi:10.48550/arXiv.2303.07823

Abstract

We derive a covariance formula for the number of excursion or level set components of a smooth stationary Gaussian field on R^d contained in compact domains. We also present two applications of this formula: (1) for fields whose correlations are integrable we prove that the variance of the component count in large domains is of volume order and give an expression for the leading constant, and (2) for fields with slower decay of correlation we give an upper bound on the variance which is of optimal order if correlations are regularly varying, and improves on best-known bounds if correlations are oscillating (e.g. monochromatic random waves).

DOI

https://doi.org/10.48550/arXiv.2303.07823

Recommended Citation

Beliaev, Dmitry; McAuley, Michael; and Muirhead, Stephen, "A Covariance Formula for the Number of Excursion Set Components of Gaussian Fields and Applications" (2023). Articles. 355.
https://arrow.tudublin.ie/scschmatart/355

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