We prove a Central Limit Theorem for the Euler-Poincar & eacute; 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 explicit calculations of the variance of the perturbed Berry's model and numerical investigations are provided to illustrate our theoretical results.
On the Euler-Poincaré Characteristic of the planar Berry's random wave: fluctuations and a perturbation study
Todino A. P.
2026-01-01
Abstract
We prove a Central Limit Theorem for the Euler-Poincar & eacute; 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 explicit calculations of the variance of the perturbed Berry's model and numerical investigations are provided to illustrate our theoretical results.File in questo prodotto:
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