Abstract
We prove convergence of Hausdorff measure of level sets of smooth Gaussian fields when the levels converge. Given two coupled stationary fields , we estimate the difference of Hausdorff measure of level sets in expectation, in terms of -fluctuations of the field . 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.
Citation
Dmitry Beliaev. Akshay Hegde. "On convergence of volume of level sets of stationary smooth Gaussian fields." Electron. Commun. Probab. 28 1 - 9, 2023. https://doi.org/10.1214/23-ECP543
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