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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Accesso online: | https://arxiv.org/abs/2307.12281 |
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| _version_ | 1866913214208409600 |
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| author | Xu, Hao Yang, Haoran Zeng, Qiang |
| author_facet | Xu, Hao Yang, Haoran Zeng, Qiang |
| contents | We consider locally isotropic Gaussian random fields on the $N$-dimensional Euclidean space for fixed $N$. Using the so called Gaussian Orthogonally Invariant matrices first studied by Mallows in 1961 which include the celebrated Gaussian Orthogonal Ensemble (GOE), we establish the Kac--Rice representation of expected number of critical points of non-isotropic Gaussian fields, complementing the isotropic case obtained by Cheng and Schwartzman in 2018. In the limit $N=\infty$, we show that such a representation can be always given by GOE matrices, as conjectured by Auffinger and Zeng in 2020. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_12281 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the expected number of critical points of locally isotropic Gaussian random fields Xu, Hao Yang, Haoran Zeng, Qiang Probability Mathematical Physics We consider locally isotropic Gaussian random fields on the $N$-dimensional Euclidean space for fixed $N$. Using the so called Gaussian Orthogonally Invariant matrices first studied by Mallows in 1961 which include the celebrated Gaussian Orthogonal Ensemble (GOE), we establish the Kac--Rice representation of expected number of critical points of non-isotropic Gaussian fields, complementing the isotropic case obtained by Cheng and Schwartzman in 2018. In the limit $N=\infty$, we show that such a representation can be always given by GOE matrices, as conjectured by Auffinger and Zeng in 2020. |
| title | On the expected number of critical points of locally isotropic Gaussian random fields |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2307.12281 |