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arXiv · 2603.05306

Maximum of sparsely equicorrelated Gaussian fields and applications

Johannes Heiny·Tiefeng Jiang·Tuan Pham·Yongcheng Qi
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Abstract

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}.

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Johannes Heiny, Tiefeng Jiang, Tuan Pham, Yongcheng Qi. 2026-03-05. Maximum of sparsely equicorrelated Gaussian fields and applications. https://arxiv.org/abs/2603.05306

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