On the excursion area of perturbed Gaussian fields
On the excursion area of perturbed Gaussian fields
We investigate Lipschitz-Killing curvatures for excursion sets of random fields on ℝ 2 under a very specific perturbation, namely a small spatial-invariant random perturbation with zero mean. An expansion formula for mean curvatures is derived when the magnitude of the perturbation vanishes, which recovers the Gaussian Kinematic Formula at the …