Maximum of sparsely equicorrelated Gaussian fields and applications
Probability
2026-03-06 v1 Statistics Theory
Statistics Theory
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 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 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}.
Keywords
Cite
@article{arxiv.2603.05306,
title = {Maximum of sparsely equicorrelated Gaussian fields and applications},
author = {Johannes Heiny and Tiefeng Jiang and Tuan Pham and Yongcheng Qi},
journal= {arXiv preprint arXiv:2603.05306},
year = {2026}
}