Difference of volume of level sets of coupled smooth Gaussian fields

Hegde Akshay, University of Oxford
Belyaev Dmitry, University of Oxford

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. This is joint work with Dmitry Beliaev.

Area: CS26 - Geometry of random fields (Michele Stecconi)

Keywords: Gaussian fields ; level sets

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