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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.01725 |
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| _version_ | 1866929371708653568 |
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| author | Di Bernardino, Elena Shevchenko, Radomyra Todino, Anna Paola |
| author_facet | Di Bernardino, Elena Shevchenko, Radomyra Todino, Anna Paola |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01725 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Euler-Poincaré Characteristic of the planar Berry's random wave: fluctuations and a perturbation study Di Bernardino, Elena Shevchenko, Radomyra Todino, Anna Paola Probability 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. |
| title | On the Euler-Poincaré Characteristic of the planar Berry's random wave: fluctuations and a perturbation study |
| topic | Probability |
| url | https://arxiv.org/abs/2406.01725 |