On the Euler-Poincar\'e Characteristic of the planar Berry's random wave: fluctuations and a perturbation study
Probability
2024-06-05 v1
Abstract
We prove the Central Limit Theorem for the Euler-Poincar\'e 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.
Keywords
Cite
@article{arxiv.2406.01725,
title = {On the Euler-Poincar\'e Characteristic of the planar Berry's random wave: fluctuations and a perturbation study},
author = {Elena Di Bernardino and Radomyra Shevchenko and Anna Paola Todino},
journal= {arXiv preprint arXiv:2406.01725},
year = {2024}
}