Maximum of sparsely equicorrelated Gaussian fields and applications
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866912945266491392 |
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| author | Heiny, Johannes Jiang, Tiefeng Pham, Tuan Qi, Yongcheng |
| author_facet | Heiny, Johannes Jiang, Tiefeng Pham, Tuan Qi, Yongcheng |
| contents | We investigate the extreme values of a sparse and equicorrelated Gaussian field on a triangle: the correlations on every vertical or horizontal line are all equal to a parameter $r \in [0,1/2]$ and are zero everywhere else. This problem is closely linked with various problems in high-dimensional statistics and extreme-value theory. We identify the threshold for $r$ at which the standard Gumbel law breaks down. Our result is based on a subtle application of the Chen-Stein method for Poisson approximation. As applications, we discuss the implication of our results on multiple testing and resolve several questions that were left open in \cite{heiny2024maximum}, \cite{tang2022asymptotic} and \cite{Jiang19}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_05306 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Maximum of sparsely equicorrelated Gaussian fields and applications Heiny, Johannes Jiang, Tiefeng Pham, Tuan Qi, Yongcheng Probability Statistics Theory We investigate the extreme values of a sparse and equicorrelated Gaussian field on a triangle: the correlations on every vertical or horizontal line are all equal to a parameter $r \in [0,1/2]$ and are zero everywhere else. This problem is closely linked with various problems in high-dimensional statistics and extreme-value theory. We identify the threshold for $r$ at which the standard Gumbel law breaks down. Our result is based on a subtle application of the Chen-Stein method for Poisson approximation. As applications, we discuss the implication of our results on multiple testing and resolve several questions that were left open in \cite{heiny2024maximum}, \cite{tang2022asymptotic} and \cite{Jiang19}. |
| title | Maximum of sparsely equicorrelated Gaussian fields and applications |
| topic | Probability Statistics Theory |
| url | https://arxiv.org/abs/2603.05306 |