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On the Euler-Poincaré Characteristic of the planar Berry's random wave: fluctuations and a perturbation study
Elena Di Bernardino, Radomyra Shevchenko, Anna Paola Todino
We prove the Central Limit Theorem for the Euler-Poincaré characteristic of Berry's random wave model in a growing domain. We also show Gaussian fluctuations for a class of Berry's…
Surface area and volume of excursion sets observed on point cloud based polytopic tessellations
Ryan Cotsakis, Elena Di Bernardino, Céline Duval
The excursion set of a smooth random field carries relevant information in its various geometric measures. From a computational viewpoint, one never has access to the continu…
On the excursion area of perturbed Gaussian fields
Elena Di Bernardino, Anne Estrade, Maurizia Rossi
We investigate Lipschitz-Killing curvatures for excursion sets of random fields on under small spatial-invariant random perturbations. An expansion formula for mean c…