On convergence of volume of level sets of stationary smooth Gaussian fields

Dmitry Beliaev; Akshay Hegde

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arXiv · 2302.10265

On convergence of volume of level sets of stationary smooth Gaussian fields

Dmitry Beliaev·Akshay Hegde

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Abstract

We prove convergence of Hausdorff measure of level sets of smooth Gaussian fields when the levels converge. Given two coupled stationary fields $f_1, f_2$ , we estimate the difference of Hausdorff measure of level sets in expectation, in terms of $C^2$-fluctuations of the field $F=f_1-f_2$. The main idea in the proof is to represent difference in volume as an integral of mean curvature using the divergence theorem. This approach is different from using Kac-Rice type formula as main tool in the analysis.

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BibTeX RIS

Dmitry Beliaev, Akshay Hegde. 2023-02-20. On convergence of volume of level sets of stationary smooth Gaussian fields. https://arxiv.org/abs/2302.10265

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