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arXiv · 2406.01725

On the Euler-Poincar\'e Characteristic of the planar Berry's random wave: fluctuations and a perturbation study

Elena Di Bernardino·Radomyra Shevchenko·Anna Paola Todino
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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.

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Elena Di Bernardino, Radomyra Shevchenko, Anna Paola Todino. 2024-06-03. On the Euler-Poincar\'e Characteristic of the planar Berry's random wave: fluctuations and a perturbation study. https://arxiv.org/abs/2406.01725

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