On the Euler-Poincaré Characteristic of the planar Berry’s random wave: fluctuations and a perturbation study
Abstract
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 mixture models that correspond to a perturbation of the initial random field. Finally, some statistical applications, explicit calculations of the variance of the perturbed Berry's model and numerical investigations are provided to support our theoretical results.
Fields of Study & Subjects
Geometry and complex manifolds
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- Latin American Journal of Probability and Mathematical Statistics
- Volume
- 23
- Issue
- 1
- Pages
- 275–275
- Publication date
- 1 January 2026
- Language
- EN