Open Access
2023 On convergence of volume of level sets of stationary smooth Gaussian fields
Dmitry Beliaev, Akshay Hegde
Author Affiliations +
Electron. Commun. Probab. 28: 1-9 (2023). DOI: 10.1214/23-ECP543

Abstract

We prove convergence of Hausdorff measure of level sets of smooth Gaussian fields when the levels converge. Given two coupled stationary fields f1,f2, we estimate the difference of Hausdorff measure of level sets in expectation, in terms of C2-fluctuations of the field F=f1f2. 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

Download 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

Information

Received: 3 March 2023; Accepted: 27 August 2023; Published: 2023
First available in Project Euclid: 27 October 2023

MathSciNet: MR4529920
Digital Object Identifier: 10.1214/23-ECP543

Subjects:
Primary: 60G15 , 60G60
Secondary: 53A07

Keywords: Gaussian fields , Level sets

Back to Top